Bulletin of the American Mathematical Society

MathSciNet review: 1567763
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Book Information:

Author: A. V. Skorohod
Title: Stochastic equations for complex systems
Additional book information: Translated by L. F. Boron, D. Reidel Publishing Company, Dordrecht, 1988, xvii + 175 pp., $69.00. ISBN 90-277-2408-3.

1.

C. Dellacherie and P. A. Meyer, Probabilities and potential, A, B, North-Holland, Amsterdam, 1975.

2.

E. B. Dynkin, Markov processes. I, II, Springer-Verlag, Berlin and New York, 1965.

Albert Einstein, Investigations on the theory of the Brownian movement, Dover Publications, Inc., New York, 1956. Edited with notes by R. Fürth; Translated by A. D. Cowper. MR 0077443

Stewart N. Ethier and Thomas G. Kurtz, Markov processes, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1986. Characterization and convergence. MR 838085, DOI 10.1002/9780470316658

Ĭ. Ī. Gīhman and A. V. Skorohod, The theory of stochastic processes. I, Corrected reprint of the first English edition, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 210, Springer-Verlag, Berlin-New York, 1980. Translated from the Russian by Samuel Kotz. MR 636254

Richard A. Holley and Daniel W. Stroock, Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions, Publ. Res. Inst. Math. Sci. 14 (1978), no. 3, 741–788. MR 527199, DOI 10.2977/prims/1195188837

Nobuyuki Ikeda and Shinzo Watanabe, Stochastic differential equations and diffusion processes, North-Holland Mathematical Library, vol. 24, North-Holland Publishing Co., Amsterdam-New York; Kodansha, Ltd., Tokyo, 1981. MR 637061

M. Kac, Foundations of kinetic theory, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. III, University of California Press, Berkeley-Los Angeles, Calif., 1956, pp. 171–197. MR 0084985

9.

O. E. Lanford, On the derivation of the Boltzmann equation, Astérisque 40 (1976), 117.

Thomas M. Liggett, Interacting particle systems, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 276, Springer-Verlag, New York, 1985. MR 776231, DOI 10.1007/978-1-4613-8542-4

H. P. McKean, Fluctuations in the kinetic theory of gases, Comm. Pure Appl. Math. 28 (1975), no. 4, 435–455. MR 395662, DOI 10.1002/cpa.3160280402

Itaru Mitoma, Generalized Ornstein-Uhlenbeck process having a characteristic operator with polynomial coefficients, Probab. Theory Related Fields 76 (1987), no. 4, 533–555. MR 917678, DOI 10.1007/BF00960073

Tokuzo Shiga and Hiroshi Tanaka, Central limit theorem for a system of Markovian particles with mean field interactions, Z. Wahrsch. Verw. Gebiete 69 (1985), no. 3, 439–459. MR 787607, DOI 10.1007/BF00532743

A. V. Skorohod, Issledovaniya po teorii sluchaĭ nykh protsessov (Stokhasticheskie differentsial′nye uravneniya i predel′nye teoremy dlya protsessov Markova), Izdat. Kiev. Univ., Kiev, 1961 (Russian). MR 0185619

Daniel W. Stroock and S. R. Srinivasa Varadhan, Multidimensional diffusion processes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 233, Springer-Verlag, Berlin-New York, 1979. MR 532498

Alain-Sol Sznitman, Équations de type de Boltzmann, spatialement homogènes, Z. Wahrsch. Verw. Gebiete 66 (1984), no. 4, 559–592 (French, with English summary). MR 753814, DOI 10.1007/BF00531891

17.

A. S. Sznitman, A fluctuation result for nonlinear diffusions, J. Funct. Anal. 56 (1984), 311-336.

Hiroshi Tanaka, Propagation of chaos for certain purely discontinuous Markov processes with interactions, J. Fac. Sci. Univ. Tokyo Sect. I 17 (1970), 259–272. MR 282410

1.

C. Dellacherie and P. A. Meyer, Probabilities and potential, A, B, North-Holland, Amsterdam, 1975.

2.

E. B. Dynkin, Markov processes. I, II, Springer-Verlag, Berlin and New York, 1965.

3.

A. Einstein, Investigations on the theory of Brownian movement, 1926. [Reprinted by Dover Publications, 1956.] MR 0077443

4.

S. Ethier and T. G. Kurtz, Markov processes: characterization and convergence, Wiley, New York, 1986. MR 838085

5.

I. I. Gihman and A. V. Skorohod, The theory of stochastic processes. I, II, III, Springer-Verlag, Berlin and New York, 1979. MR 636254

6.

R. A. Holley and D. W. Stroock, Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions, Publ. Res. Inst. Math. Sci. 14 (1978), 741-788. MR 527199

7.

N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland, Amsterdam (Kodansha ltd., Tokyo), 1981. MR 637061

8.

M. Kac, Foundations of kinetic theory, Proc. Third Berkeley Sympos. on Math. Stat. and Prob. 3 (1956), 171-197. MR 84985

9.

O. E. Lanford, On the derivation of the Boltzmann equation, Astérisque 40 (1976), 117.

10.

T. M. Liggett, Interacting particle systems, Springer-Verlag, Berlin and New York, 1985. MR 776231

11.

H. P. McKean, Fluctuations in the kinetic theory of gases, Comm. Pure Appl. Math. 28(1975), 435-455. MR 395662

12.

I. Mitoma, Generalized Ornstein-Uhlenbeck process having a characteristic operator with polynomial coefficients, Prob. Theory Related Fields 76 (1987), 533-555. MR 917678

13.

T. Shiga and H. Tanaka, Central limit theorem for a system of Markovian particles with mean field interactions, Z. Wahrsch. Verw. Gebiete 69 (1985), 439-459. MR 787607

14.

A. V. Skorohod, Studies in the theory of random processes, Addison-Wesley, Reading, Mass., 1965. [Reprinted by Dover Publications, New York.] MR 185620

15.

D. W. Stroock and S. R. S. Varadhan, Multidimensional diffusion processes, Springer-Verlag, Berlin and New York, 1979. MR 532498

16.

A. S. Sznitman, Equations de type Boltzmann, spatialement homogènes, Z. Wahrsch. Verw. Gebiete 66 (1984), 559-592. MR 753814

17.

A. S. Sznitman, A fluctuation result for nonlinear diffusions, J. Funct. Anal. 56 (1984), 311-336.

18.

H. Tanaka, Propagation of chaos for certain purely discontinuous processes with interaction, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 17 (1970), 259-272. MR 282410