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Book Review

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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.

References [Enhancements On Off] (What's this?)

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  • 2. E. B. Dynkin, Markov processes. I, II, Springer-Verlag, Berlin and New York, 1965.
  • 3. 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
  • 4. 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
  • 5. 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
  • 6. 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, 10.2977/prims/1195188837
  • 7. 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
  • 8. 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 and Los Angeles, 1956, pp. 171–197. MR 0084985
  • 9. O. E. Lanford, On the derivation of the Boltzmann equation, Astérisque 40 (1976), 117.
  • 10. Thomas M. Liggett, Interacting particle systems, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 276, Springer-Verlag, New York, 1985. MR 776231
  • 11. H. P. McKean, Fluctuations in the kinetic theory of gases, Comm. Pure Appl. Math. 28 (1975), no. 4, 435–455. MR 0395662
  • 12. 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, 10.1007/BF00960073
  • 13. 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, 10.1007/BF00532743
  • 14. A. V. Skorokhod, Studies in the theory of random processes, Translated from the Russian by Scripta Technica, Inc, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0185620
  • 15. 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
  • 16. 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, 10.1007/BF00531891
  • 17. A. S. Sznitman, A fluctuation result for nonlinear diffusions, J. Funct. Anal. 56 (1984), 311-336.
  • 18. 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 0282410

Review Information:

Reviewer: Donald Dawson
Journal: Bull. Amer. Math. Soc. 20 (1989), 259-267
DOI: https://doi.org/10.1090/S0273-0979-1989-15790-X