1. Reliability of aging system, Ann. Univ. Sofia, Fac. Math. Mec., Vol. 68 (1973/74), 1977, 339-347 (in Russian).
2. Theorems for moments and their applications for NBU distributions, in:
Mathematics and Mathematical Education. Proc. of Fourth Spring Conference of
Bulgarian Mathematical Society, Pernik, April 2-4, 1975, 1978, 303-310
3. Maximum likelihood estimation of U-type failure rate function, Annuaire
Univ. Sofia, Fac. Math. Mec. Vol. 72, 127-140 (in Russian).
4. Hausdorff metric structures of the space of probability measures,
Zap. Nauchn. Sem. Leningrad. Otdel Mat. Inst. Steklov. (LOMI), Vol. 87,
1979, 87-103 (in Russian); English transl., J. Soviet Math., Vol. 17, 1981,
5. Lévy-Prokhorov distance in a space of semi-continuous set
functions, in: Stability Problems for Stochastic Models, Proceedings,
Moscow, VNIISI, 1980, 76-88 (in Russian);
English transl., J. Soviet Math., Vol. 32, No. 1, 1986, 64-74.
6. On minimal metrics in a space of real-valued random variables,
Dokl. Akad. Nauk USSR, 1981, Vol. 257, No. 5, 2067-2070 (in Russian);
English transl. Soviet Math. Dokl., Vol. 23, No. 2, 1981, 425-428.
7. Minimal metrics in a space of random vectors with fixed one-dimensional
marginal distributions, in: Stability Problems for Stochastic Models, Proceedings,
Moscow, VNIISI, 1981, 112-128 (in Russian); English transl., J. Soviet Math.,
Vol. 34, No. 2, 1
8. Minimal metrics in the minimal variables spac. Pub. Inst. Statist.
Univ. Paris, Vol. XXVII, fasc. I, 1982, 22-47.
9. Minimal metrics in the random variables space, in: Probability and
Statistical Inference, Proceedings of the 2nd Pannonian Symp. Ed. by Grossman
M. et al. Dodrecht; D. Reidel Publ. Company, 1982, 318-327.
10. Metrics that are invariant relative to monotone transformations (with
D. Vandev and C. Ignatov), in: Stability Problems for Stochastic Models,
Proceedings, Moscow, VNIISI, 1982, 25-36 (in Russian); English transl.
J. Soviet Math., Vol. 35, No. 3, 198
11. Stability of an exponential law characterization (with B. Dimitrov
and L. Klebanov), in: Stability Problems for Stochastic Models, Proceedings,
Moscow, VNIISI, 1982, 39-46 (in Russian); English transl., J. Soviet Math.,
Vol. 35, No. 3, 1986, 2479-2485.
12. Stochastic inequalities for p-functions (with A. Obretenov), Dokl.
Bulgarian Acad. Sci., 1982, Vol. 35, No. 5, 613-616.
13. Minimality of ideal probabilistic metrics (with Zv. Ignatov), in:
Stability Problems for Stochastic Models, Proceedings, Moscow, VNIISI, 1983,
36-48 (in Russian); English transl., J. Soviet Math., Vol. 32, No. 6, 1986,
14. Stability of the service process in a system of type M/M/1 (with A.
Obretenov and B. Dimitrov), in: Stability Problems for Stochastic Models,
Proceedings, Moscow, VNIISI, 1983, 71-79 (in Russian); English transl., in
J. Soviet Math., Vol. 32, No. 6,
15 Stability of some characterization properties of the exponential
distribution (with A. Obretenov), in: Stability Problems for Stochastic
Models, Proceedings, Moscow, VNIISI, 1983, 79-87 (in Russian); English
transl., in J. Soviet Math., Vol. 32, No. 6
, 1986, 643-651.
16. Minimal metrics in the real valued random variables space, Lect.
Notes Math., (Springer-Verlag), 1983, Vol. 982, 172-180.
17. Existences and uniqueness of the limit Gibbsian distribution (G.
Chobanov), in: Lectures on Stochastic Problems of the Modern Physics, Sofia,
Univ. Sofia, 1983, 42-60 (in Bulgarian).
18. Compactness in the probability measures space, in: Proceedings of the
Third European Young Statisticians Meeting, Ed. by Galyare M. et al., Leuven:
Katholieke Univ., 1983, 148-152.
19. Characterization of the bivariate exponential distribution and
Marshall-Olkin distribution and stability (with A. Obretenov) Lect. Notes
Math., (Springer-Verlag), 1983, Vol. 982, 136-150.
20. On a problem of Dudley, Dokl. Akad. Nauk., 1984, Vol. 275, No. I,
28-31 (in Russian); English transl. in Soviet Math Dokl., 1984, Vol. 29,
No. 2, 162-164.
21. On a class of minimal functionals in a space of probability measure,
Teor. Verojatnot. i Primen., Vol. 29, No. 1, 1984, 41-48 (in Russian); English
transl., in Theor. Probab. Appl., Vol. 29, No. 1, 41-49.
22. The Monge-Kantorovich mass transference problem and its stochastic
applications (invited paper), Teor. Verojatnost. i Primen., Vol. 29, No. 4,
625-653 (in Russian); English transl., in Theor. Prob. Appl. Vol. 29, No. 1,
23. On the (-structure of the average and uniform distances, Dokl. Akad.
Nauk, Vol. 278, No. 2, 282-285 (in Russian); English transl., in Soviet Math.
Dokl., Vol. 30, 1984, No. 2, 369-372.
24. Ideal quadratic metrics (with Zv. Ignatov), in: Stability problems
for Stochastic Models, Proceedings, Moscow, VNIISI, 1984, 119-128 (in Russian);
English transl., J. Soviet Math., Vol. 35, 1986, No. 2, 2376-2394.
25. Characterization problems in queueing and their stability (with V.
Kalashnikov), in: Stability Problems of Stochastic Models, Proceedings,
Moscow, VNIISI, 49-86 (in Russian); English transl., J. Soviet Math.,
Vol. 35, No. 2, 1986, 2336-2360.
26. Hausdorff metric construction in the probability measures space,
Pliska, Vol. 7, 152-162.
27. Maximum likelihood estimation of the mortality rate function (with
B.N. Dimitrov and A. Yu. Yakovlev), Biom. J., Vol. 27, 1985, 317-326.
28. Extreme functionals in the space of probability measure, Lecture Notes
in Math., (Springer-Verlag), Vol. 1155, 320-348.
29. Characterization problems in queueing and their stability (with V.V.
Kalashnikov), Adv. Appl. Prob., 17, 320-348.
30. Stability of lack of memory property of multivariate exponential
distributions in finite number of points (L.B. Klebanov), Lect. Notes Math.,
(Springer-Verlag), Vol. 1155, 131-143.
31. Rate of convergence in limit theorems for the Max-scheme (with V.M.
Zolotarev), Lect. Notes Math., (Springer-Verlag), Vol. 1155, 415-442.
32. Uniformity in weak and vague convergences, Teor. Verojatnost i Primen.,
Vol. 30, No. 3, 1985, 538-541 (in Russian); English transl., Theor. Prob. Appl.,
Vol. 30, 573-576.
33. Stability in the mean of the characterization of queueing models
(with V.V. Kalashnikov), in: Stability Problems for Stochastic Models,
Proceedings Moscow, VNIISI, 1985, 67-75 (in Russian);
English transl., J. Soviet Math., Vol. 40, No. 4, 1988, 502- 509.
34. Bounds of deviation from exponentiality of distribution function
classes (with A. Obretenov), Proceedings of 14th Spring Conference of the
Union of Bulgarian Mathematicians, Sunny Beach, April 1985, 495-501.
35. Probability Metrics and Their Applications to the Problems of
Stability for Stochastic Models. Author-review on the Doctor of Science
Dissertation, Moscow, Steklov Mathematical Institute, 1985.
36. Characterization of queueing models and their stability
(with V.V. Kalashnikov), in "Probability Theory and Mathematical
Statistics," Prokhorov et al. (eds.), UNU Science Press, Vol. 2, 1986, 37-53.
37. Characterization of inverse problems in queueing and their
stability (with V.V. Kalashnikov), J. Appl. Prob., Vol. 23, 1986, 459-473.
38. New methods for comparison of volume functions of historical
texts (with A.T. Fomenko and V.V. Kalashnikov), in: Stability Problems
for Stochastic Models, Proceedings, Moscow, VNIISI, 1986, (in Russian), 33-45.
39. Extremal functionals in a space of probability measures. Summary
of the report presented at the seminar of A.V. Skorokhod, Theor. Prob. Appl.,
Vol. 33, 1986, 540.
40. On the optimal duality usage (with B.N. Dimitrov). Proceedings IV
International Conference on Statistical Methods in Experimental Design and
Quality Control, Vol. 2, VARNA, 1986, 5-10.
41. Extreme functional in the space of Probability Theory and Mathematical
Statistics," Prokhorov et al. (eds.) VNU Science Press, Vol. 2, 1986, 471-476.
42. Metrization of the vague convergence (with G.S. Chobanov), Pliska,
No. 2, 1986, 1154-158 (in Russian).
43. Estimates of the deviation between the exponential and new classes
of bivariate distributions (with A. Obretenov). Lect. Notes in Math.,
(Springer-Verlag), Vol. 1233, 1987, 93-102.
44. The problems of stability in insurance mathematics (with J. Beirlant),
Insurance: Mathematics & Economics, Vol. 6, 1987, 179-188.
45. Probability metrics and their application to problems of stability of
stochastic models. Proceedings of the Sixteenth Spring Conference of their
Union of Bulgarian Mathematicians, Sunny Beach, April, 1987, 53-60.
46. An ideal metric and the rate of convergence to a self-similar process
(with M. Maejima), Ann. Probability, Vol. 15, 1987, 702-727.
47. On the rate of convergence in extreme value theory (with E. Omey),
Theor. Prob. Appl., 1988, 33, 560-565.
48. Theoretical bounds for radiation therapy efficiency (with A. Yu.
Yakovlev), Medical Radiology, No. 5, Moscow, 1988, 17-21 (in Russian).
49. Some problems of the competing risks theory, (with A. Yu. Yakovlev),
in: Proceedings of the Fifth International Summer School on Probability
Theory and Mathematical Statistics, Varna, 1985. Publishing House of the
Bulgarian Academy of Sciences, Sofia, 1988, 171-187.
50. Theoretical bounds for the tumor treatment efficiency (with A. Yu.
Yakovlev), Syst. Anal. Model Simul. 5, 1988 1, 37-42.
51. An estimate of the rate of convergence to the limit distribution for
the minima scheme for random number of identically distributed random
variables (with L.B. Klebanov and A. Yu. Yakovlev) in: Stability Problems
for Stochastic Models, Proceedings, Moscow, VNIISI, (in Russian), 1988, 120-124.
52. The stability of stochastic models (invited paper) Applied Probability
Newsletter, Vol. 12, No. 2, 1988, 3-4.
53. Bounds for crude survival probabilities within competing risks
framework and statistical application (with A. Yu. Yakovlev), Statistics
and Probability Letters, 389-394.
54. Bounds for the probabilistic characteristics of latent failure times
within competing risks framework (with A. Yu. Yakovlev), Serdica, Vol. 14,
55. On the statistical inference from survival experiments with two
types of failure (with A. Yu. Yakovlev, N.O. Kadyodva, E.M. Myasmikova)
Biom. J. 30/7, 1988, 835-842.
56. Rates for CLT via new ideal metrics (with J. Yukich), Annals of
Probability, 17, 1989, 775-788.
57. Estimates of the rate of convergence for max-stable processes
(with L. de Haan), Annals of Probability, 17, 1989, 651-677.
58. Classification problem for probability metric (with R.M. Shortt).
Contemporary Mathematics, 94, 1989, 221-262.
59. Stable distributions for asset returns (with S. Mittnik). Appl. Math.
Lett. 2/3, 1989, 301-304.
60. Analysis of the survival rate after the combined radiation effect.
Synergism and antagonism of the effects of two factors (with E.M. Myasnikova,
A. Yu. Yakovlev et al). Radiology, Vol. 4, 1989, 478-483 (in Russian).
61. Precise upper bounds for the functionals describing tumor treatment
efficiency (with L.G. Hanin, R.E. Goot, and A. Yu. Yakovlev) Lecture Notes
in Math., Vol. 1412, 1989, Springer-Verlag, 5-67.
62. A characterization of random variables with minimum L2-distance
(with L. Rüschendorf), J. Mult. Analysis, Vol. 132, 1989, 48-54.
63. On the products of a random number of random variables in connection
with a problem from mathematical economics (L.B. Klebanov and J.A. Melamed).
Lecture Notes in Math., Vol. 1412, 1989, Springer-Verlag, 103-109.
64. The problem of stability in queueing theory. (Invited paper) Queueing
Systems Theory and Applications, Vol. 4, 1989, 287-318.
65. New duality theorems for marginal problems with some applications in
stochastics (with V.L. Levin). Lecture Notes in Math., Vol. 1412,
Springer-Verlag, 1989, 137-170.
66. Smoothing metrics for measures on groups (with J. Yukich). Annales
de l'Institut Henri Poincare, 25, 1989, 429-441.
67. Maximum likelihood estimation of the bimodal failure rate for censored
and tied observations (with A. Yu. Yakovlev and N.O. Kadyrova), Statistics,
Vol. 20, 1989, 135-140.
68. Isotonic maximum likelihood estimation of the bimodal failure rate -
a computer-based study (with N.O. Kadyrova and A. Yakovlev), Statistics,
Vol. 20, 1989, 271-278.
69. Explicit solutions of moment problems (with I. Kuznezova-Sholpo).
Probability and Math. Statistics, Vol. 10, 1989, 297-312.
70. Approximation of random queue by means of deterministic queueing
models (with G. Anastassiou). Approximation Theory VI, C.K. Chui, L.L.
Schumaker, and J.D. Ward) (eds.), 1989. Academic Press, New York, 1-4.
71. On the rate of convergence of some functionals of a stochastic
process (with P. Todorovic) J. Appl.Prob. 28, 1990, 805-814.
72. A counter-example to a.s. constructions (with L. Rüschendorf).
Statistics and Probability Letters 9, 1990, 307-309.
73. Approximation of sums by compound Poisson distributions with respect to
stop-loss distances (with L. Rüschendorf), Adv. Appl. Prob. 22, 1990, 350-374.
74. A transformation property of minimal metrics (with L. Rüschendorf).
Theory Prob. Appl. 35, 1990, 131-137.
75. Duality theorems for Kantorovich-Rubenstein and Wasserstein functionals
(with R.M.Shortt). Dissertationes Mathematicae, 1990, Vol. 299.
76. A note on the stability of the estimation of the distribution (with
L. Baxter), Probability and Statistics Letters, Vol. 10, 1990, 37-41.
77. Association of stable random variables (with Lee Mei-Ling Ting and
G. Samorodnitski), Annals of Probability, 18, 4, 1990, 1759-1764
78. Volume functions of historical (narrative) texts and the amplitude
correlation principle (with A.T. Fomenko), Computers and Humanities, 24/3,
79. Some statistical test associated with the concept of delta-stochastic
ordering of two random variables (with R.E.Good, A.Yu. Yakovlev, N.O.
Kadyrovaand G.M. Zharinov) Serdica, Bulgaicae mathematicae publicationes,
16, 1990, 240-245.
80. Rates of convergence of (-stable random motions (with J.E. Yukich).
Journal of Theoretical Probability, 4, 1991, 333-352.
81. Alternative multivariate stable distributions and their application
to financial modeling (with S. Mitnik), in: Stable Processes and Related
Topics. Proceedings of MSI Workshop on Stable Processes and Related Topics.
Ed. S. Cambanis et al., Birkhauser, Boston, 1991, 107-119.
82. Approximate independence of distributions on spheres and their
stability (with L. Rüschendorf), Annals of Probability, vol 19, 1991, 1311-1337.
83. Max-geometric infinite divisibility and stability (with S. Resnick).
Stochastic Models, 2, 1991, 191-218.
84. Rates of convergence in multivariate extreme value theory (with E.
Omey). Journal of Multivariate Analysis, 37, 1991, 36-50
85. The stability of a characterization of the bivariate Marshall-Olkin
distribution (with L. Baxter). Journal of Mathematical Analysis and
Applications, 160, 1991, 563-571.
86. Recent results in the theory of probability metrics (with L.
Rüschendorf), Statistics & Decisions 9, 1991, 327-373.
87. Mass transshipment problems and ideal metrics. Numer. Funct. Anal.
and Optimiz., 12 (5&6), 1991, 563-573
88. Optimal mass transportation problems. Proceedings of XI Congreso de
Metodologias en Ingenieria de Sistemas. 115-120, 1991, Azocar, Santiago de Chile.
89. Uniformities for the convergence in law and in probability (with L.
Rüschendorf and A. Schief), Journal of Theoretical Probability, 5, 1992, 33-44
90. Moment problems and their applications to characterization of
stochastic processes, queueing theory and rounding problems (with G.A.
Lecture Notes in Pure and Applied Mathematics, v.138, "Approximation theory",
1-77, 1992, Marcel Dekker, New York.
91. Kantorovich's functionals in space of measures (with M. Taksar), in
Applied Stochastic Analysis, Proceedings of the US-French Workshop, I.Karatzas
and D. Ocone (eds), Lecture Notes in Control and Information Science, vol 177, 1992, 248-261.
92. Geometric stable distributions and Laplace-Weibull mixtures
(with A. SenGupta), Statistics & Decisions, v.10, 1992, 251-271
93. Moment problems and their applications to the stability of queueing
models (with G. Anastassiou), Computes and Mathematics with Applications, 24,
No 8/9, 1992, 229-246.
94. A new ideal metric with applications to multivariate stable limit
theorems (with L. Rüschendorf), Probability Theory and Related Fields, 94,
95. A probabilistic approach to optimal quality usage (with B. Dimitrov
and Z. Khalil), Computers and Mathematics with Applications, 24, No.8/9, 1992,
96. Rate of convergence for sums and maxima and doubly ideal metrics (with
L. Rüschendorf), Theory of Probab. Appl., 37,2, 1992, 276-289.
97. Theory of probability metrics and recursive algorithms, in Distancia
'92, Proceedings of Congres International sur Analyse en Distance,
(ed. S. Joly and G. le Calve), Universite de Haute Bretagne, Rennes,
98. On Lp- minimal metric (with A. Schief). Probability and Mathematical
Statistics, vol. 13, fasc. 2, 1992, 311-320.
99. Dependence of stable random variables (with Lee,M.-L.T. and G.
Samorodnitsky), Stochastic Inequalities, IMS Lecture Notes - Monograph
Series, 22, 1993, 219-234.
100. On the optimal control of cancer radiotherapy for nonhomogeneous
cell populations (with L. Hanin and A. Yu. Yakovlev) Advances of Applied
Probability, 25, 1993, 1-23.
101. Random minima scheme and carcinogenic risk estimation (with A.
Yu. Yakovlev), Mathematical Scientist, 18, 1993, 20-36.
102. Book Review of "Stationary Stochastic Models", by A. Brandt,
P. Franken and B. Lisek, John Wiley & Sons, 1990, p. 344, in:
Metrika-International Journal for Theoretical and Applied Statistics,
40, 1993, 130-132.
103. Some developments on the theory of rounding proportions (with
M. Balinski and B. Athanasopoulos) Bulletin of the ISI, 49th Session,
Firenze, 1993, Book 1, 71-72.
104. Laplace-Weibull mixtures for modeling price changes,
(with A. SenGupta) Management Science, 1993, 1029-1038.
105. On constrained transportation problems (with L. Rüschendorf).
Proceedings of the 32nd Conference on Decision and Control, IEEE Control
Systems Society, v.3, 2896-2900.
106. A stochastic model of radiation carcinogenesis: latent time
distributions and their properties (with L.B. Klebanov and A. Yu. Yakovlev),
Mathematical Biosciences, 113, 1993, 51-75.
107. Rounding proportions: rules of rounding (with M. Balinski),
Numerical Functional Analysis and Optimization, 14, 1993, 475-501.
108. U-statistics of random-size samples and limit theorems for systems
of Markovian particles with non-Poisson initial distributions
(with R. Epstein Feldman), Ann. of Probability, 21, 1993, 1927-1945.
109. Rate of convergence of maxima of random arrays with applications
to stock returns, Statistics & Decisions, 11, 1993, 279-288.
110. On the parametric estimation of survival functions
(with L.B. Klebanov and A. Yu. Yakovlev), Statistics & Decision,
Suppl. Issue 3, 1993, 83-102.
111. Option pricing formulae for speculative prices modelled by
subordinated stochastic processes, PLISKA (Studia Mathematika Bulgarica,
Bulgarian Academy of Sciences), 19, 1993, 175-190.
112. Modeling asset returns with alternative stable laws,
(with S. Mittnik) Econometric Reviews, 12(3), 1993, 261-330.
113. Reply to comments on "Modeling asset returns with alternative
stable laws" and some extensions, (with S. Mittnik) Econometric Reviews,
1993, 12(3), 1993 347-389.
114. Test on association of random variables in the domain of attraction
of multivariate stable law, (with H. Xin) Probability and Mathematical
Statistics, vol. 14, Fasc. 1, 1993, 125-141.
115. Stable models for asset returns and option pricing, QUICK, ORI
Report, 8(11), 1993, 24-26 (in Japanese).
116. Maximum submatrix traces for positive definite matrices
(with I. Olkin) SIAM Journal of Matrix Analysis Applications,
vol. 14, 1993, 390-397.
117. On the rate of convergence in the CLT with respect to the
Kantorovich metric (with L. Rüschendorf), Probability in Banach
Spaces 9, Birkhäuser, Boston-Basel-Berlin, (edt. J. Hoffman- Jorgensen,
J. Kuelbs, M.B. Markus), 1994, 1993-207.
118. On the Cox, Ross and Rubinstein model for option pricing
(with L. Rüschendorf), Theory of Probabl. Appl., 39, 1994, 150-190.
119. Stable models in testable asset returns (with B. Gamrowski) in
"Approximation, Probability and Related Fields", Plenum Press, 1994, 223-236.
120. Geometric stable distributions in Banach spaces (with G. Samorodnitsky).
Journal of Theoretical Probability, 7(2), 1994, 351-373.
121. On the joint estimation of stable law parameter (with L.B. Klebanov
and J.A. Melamed), in "Approximation, Probability and Related Fields", Plenum,
1994. Press, N.Y., 1994, 315-320.
122. Multivariate probabilistic wavelet approximation (with G. Anastassiou
and X. M. Yu), in "Approximation, Probability and Related Fields", Plenum
Press, N.Y., 1994, 657.
123. The theory of geometric stable distributions and its use in modelling
financial data (with T. J. Kozubowski) European Journal of Operations
research: Financial Modelling, 74, 1994, 310-324.
124. Propagation of chaos and contraction of stochastic mappings (with L.
Rüschendorf) Siberian Advances in Mathematics, 1994, 4, 114-150.
125. Solution of some transportation problems with relaxed or additional
constraints (with L. Rüschendorf), SIAM Journal on Control and Optimization,
1994, vol. 32, No. 3, 673-689.
126. Limit theorems for recursive algorithms (with P. Feldman and
L. Rüschendorf) Journal of Computational and Applied Mathematics, 1994, 56,
127. Mass transshipment problems and ideal metrics (with L.G. Hanin).
Journal of Computational and Applied Mathematics, 1994, 56, 183-196.
128. Multivariate stable futures prices (with B. Cheng), Mathematical
Finance, 1995, 5, 133-153.
129. A bivariate limiting distribution of tumor latency time, (with
Chufang Wu and A. Yu Yakovlev), Mathematical Biosciences.
Papers Accepted for Publication:
1. The methods of moments in computer tomography (with L. B. Klebanov),
Math. Scientists, 20, 1995.
2. A generalized binomial model and option formulae for subordinated
stock-price processes (with R. Karandikar), Probability and Mathematical
3. Testing multivariate symmetry (with C.R. Heathcote and B. Cheng),
Journal of Multivariate Analysis, 1995.
4. Rates of convergence in the operator-stable limit theorem
(with M. Maejima), Journal of Theoretical Probability.
5. Proximity of probability measures with common marginals in a
finite number of directions (with L.B. Klebanov), Proceedings "Distributions
with Given Marginals", IMS, 1994.
6. Probability metrics and recursive algorithms (with L. Rüschendorf)
Journal of Applied Probability.
7. Limit laws for a stochastic process and random recursion arising in
probabilistic modelling, (with G. Samorodnitsky), Journal of Applied
8. Characterization of monomial and linear forms with random
coefficients (with L. B. Klebanov and R. Shimizu), Journal of Statistical
Planning and Inference, 1995.
9. Modelling Financial Assets with Alternative Stable Models
(with S. Mittnik), Wiley Series in Financial Economics and Quantitative
Analysis, Wiley, 1995.
10. Transportation Problems in Probability Theory (with L. Rüschendorf),
Springer, New York, 1996.
||Mathematical Methods for Construction for Queueing Models
(with V.V. Kalashnikov), Moscow, Nauka, 1988, (in Russian)
||English translation., Wadsworth & Brooks/Cole Advanced Books, 1990.
|| Quantitative Criteria for Convergence of Measures
(with A. Kakosyan and L. Klebanov), Erevan, Ajastan Press, 1987,
||English translation. Springer-Verlag, (to appear).
||Probability Metrics and the Stability of Stochastic Models, Wiley,
Chichester, New York, 1991.
||Approximation, Probability and Related Fields, (with G. Anastassiou), Plenum Press, N.Y., 1994.
Applied Analysis and Stochastics (with G.A. Anastassiou) Journal of Computational and Applied Mathematics, Vol. 40, No. 2, 137-252.
"Stochastic Programming: Stability, Numerical Methods and Applications" (with W. Römisch), Journal of Computational and Applied Mathematics, 56, 1-2, 1994.
Professional Consulting and Advising
1990 "Geometric Stable Laws and Laplace-Weibull Mixtures in Modeling the Real Estate Prices in Paris", for Laboratoire d'Econometrie de l'Ecole Polytechnique and Chambre des Notaires de Paris.
1989, 1991 "Stable Models for Asset Returns", for Kepler - Financial Services, Stony Brook, New York, President J. Simon.
1992 "Stable Portfolios and Option Pricing", for AXCOM - Financial Services, Berkeley, President A. Berkelamp.
1993 "Bubbles in the land-prices in Japan", for QUICK Institute, Tokyo.
Research Direction 1:
The theory of probability metrics:
This is the main direction of my research until 1991. Two independent reviews follow:
L. Rüschendorf for Zentralblatt fur Mathematik Mathematical Abstracts: vol. 744, May, 1993 Rachev S.T.: Probability metrics and the stability of stochastic models, Wiley Series in Probability and Mathematical Statistics.
"Approximation and stability problems are basic problems in probability theory and its applications. The author makes an impressive and successful attempt to explain that it is useful to know a great variety of probability metrics and to know about their
structural and topological properties in order to solve these problems. The book contains a wealth of recent or new theoretical results and applications, ranging from problems on the rate of convergence in limit theorems to the qualitative and quantitat
ive analysis of the stability of stochastic models as e.g. the stability of queueing models or the stability of characterization results in probability theory. Further applications are to approximation problems in risk theory and operations research. It
unifies many seemingly different problems in probability theory.
The treatment of relations between different probability metrics is based on dual and explicit solutions of the classical Monge-Kantorovich type problems. Some classical results in this direction are the Strassen-Dudley representation of the total variat
ion metric due to Dobrushin, related to many coupling arguments. There are interesting recent developments on multivariate coupling problems, generalizations of Skorohod's a.s. representation theorem, on Glivenko-Cantelli
type results on uniform convergence and on Frechet-bounds.
Some basic notions and the results in the theory of probability metrics were introduced by Zolotarev.
The present book elaborates this approach in full depth and demonstrates its potential and actual usefulness. It enriches the probability theory by new
results and new directions of work,
poses some challenging open problems, and establishes the theory of probability
metrics as a valuable subject in probability theory.
Without a doubt it will be a basic orientation and reference point for future work in the field of approximation problems in probability theory.
The book is well organized and very readable. The author can be congratulated for his authentic and important work."
L. Heinrich for Book review section in "Statistics", March, 1993
S.T. Rachev: Probability Metrics and the Stability of Stochastic Models J. Wiley & Sons, Chichester-New York, 494 pp.
"The study of limit theorems and a great number of other questions in pure and applied probability and in statistics makes it necessary to introduce functions, defined either on classes of probability distributions or on classes of random elements, and ev
aluation, or at least estimating, their nearness in one or another probabilistic sense. In probability theory, metrics have been used for a long time, although one usually exploits a very limited class of metrics such as the Levy-Prokhorov metric, the un
iform (or Kolmogorov) metric and Lp-metrics. On the other hand, some ideas of the method of metric distance have been developed in approximation theory and functional analysis. Rachev's book presents the most extensive and deepest treatment theory of pr
obability metrics from probabilistic and functional-theoretic point of view. A further conspicuous feature of this book consists in modifying and demonstrating the problems and the obtained results, respectively, in relevant situations of quite different
fields of application such as stability problems in risk theory, stability and approximation of queueing systems, robustness problems, coupling techniques, rates of convergence for sums and maxima of i.i.d. random vectors, etc. In order to classify the
set of probability metrics the author's concept is organized as follows:
(i) Description of the basic structures of probability metrics,
(ii) Analysis of the topologies in the space of probability measures generated by different types of probability metrics,
(iii) Characterization of "ideal" metrics for the given problem,
(iv) Investigations of the main relationships between different types of probability metrics.
Much attention is paid to the possibility of giving equivalent definitions of probability metrics (for example, in direct and dual terms, in terms of the Hausdorff metric on sets, etc.). This is often a decisive point in concrete applications.
To keep the overview about the huge material delivered, all considered
probability (semi-) distances are summarized at the end of the book.
The reader interested in a deeper insight into applications only
touched in the 19 chapters is referred to more than 600 references which
contains more detailed information. This book can be recommended to graduate
students and researchers in probability theory and its applications
(in particular in operations research) to all which are familiar to some
extent with measure theory and functional analysis."
RESEARCH DIRECTION 2: Mass transportation problems.
A description of this direction of research is given in the recent review
sent to me by Dr. Martin Gilchrist (Senior Editor - Springer Verlag) along
with the contract for writing a new monograph "Mass Transportation Problems in
Probability Theory" (Springer, Series: Applied Probability, to appear
"It is a pleasure to see that Zari Rachev has finally got around to writing
the definite, encyclopedic treatise on mass transport problems. Certainly,
no one is a qualified to write such a book as he: Zari has devoted his
entire professional career to the study of this circle of problems and is
widely recognized as a leader in the field. Perhaps only Zolotarev could
make claim to similar status. It is for this reason that I think there will
be a considerable demand for the book, at least if it is properly marketed.
As is evident from the first pages, this is a far reaching topic with
connections to a great many areas of mathematics, and so I believe it is of
importance to target a very broad audience: not only probabilists and
statisticians, but also measure theorists, functional analysis, specialists
in linear programming and optimization, and perhaps even combinatorists and
those in operations research. (When I mention combinatorics, I have in
mind the interconnections between this area and matching theory, marriage
problems, and the like.)
The book is written at a high level of sophistication and assumes the same
from the reader. A very good background in measure theory and
measure-theoretic probability is required, as well as a knowledge of
functional analysis, linear programming, and linear optimization and duality.
Even where these are not specifically necessary to follow a proof, reading
this book would be, I think, very rough going to someone who had not seen
such topics before. Motivation is given here only in minimal doses. It is
therefore above the level usual in most graduate texts, although I could
imagine portions of it in a graduate research seminar. The question, I
suppose, is whether this is meant as an introductory text leading into more
advanced areas, or rather a research monograph, or again rather as an
encyclopedia volume on mass transport. As it now appears, it seems to be
the later . . . "
RESEARCH DIRECTION 3: Modeling and statistical analysis of radiation-induced risk
This topic covers 19 published joint papers with Prof. A. Yakovlev.
Seven of the papers appeared in journals in the period 1989-1990.
Yakovlev, who was recently elected to membership of the prestigious Russian
Academy of Sciences, was awarded the Yamagiwa-Yoshida Cancer Study Grant of
the International Union against Cancer to work with me at UCSB for a period
of four months. For my joint work with Yakovlev I have received a Honorary
Doctorate from St. Petersburg's Technical University.
RESEARCH DIRECTION 4: Modeling price changes and option pricing.
This a new direction of my research; so far I have published only four
papers, starting in 1989, though many more are submitted or in preparation.
Soon a monograph (jointly written with Stefan Mittnik, Econ. Dept., SUNY) on
this topic will appear in Wiley.
I was teaching a PhD level course "Mathematical Finance-Probabilistic Models",
at the Ecole Polytechnique-University of Paris 1 (Pantheon-Sorbonne), and I
have a PhD student here working on this field.
RESEARCH DIRECTION 5: Rounding problems and fair representation.
This is a very recent joint work with M. Balinski (Ecole Polytechnique).
The research is across disciplinary lines - developing the use of ideas
that come from the mathematical theory of fair representation (a theory
which has its origins in the equitable allocation of seats in a Congress
or Parliament and that has recently been used in a Supreme Court decision)
to problems in probability and statistics - and developing the use of ideas
that come from probability metrics to problems of rounding, of reporting
data and of equity. It is a surprisingly fertile marriage of very different
ideas and methods, motivated by problems that are really quite new and are