Book Review

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Book Information:

Author: N.V. Krylov

Title: Introduction to the theory of diffusion processes

Additional book information: Transl. Math. Monographs, vol. 142, Amer. Math. Soc., Providence, RI, 1995, xi + 271 pp., ISBN 0-8218-4600-0, $95.00

**1.**L. Bachelier,*Théorie de la spéculation*, Ann. Sci. École Norm. Sup.**17**(1900), 21-86.**2.**R. Brown,*A Brief Account of Microscopical Observations Made in the Months of June, July, and August, 1827, on the Particles Contained in the Pollen of Plants; and on the General Existence of Active Molecules in Organic and Inorganic Bodies*, Philosophical Magazine N. S.**4**(1928), 161-173.**3.**J. Crank,*The Mathematics of Diffusion*, Oxford at the Clarendon Press (1956). MR**18:616c****4.**A. Einstein,*On the Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat*, Ann. Physik**17**(1905) [See also A. Einstein:*Investigations on the Theory of the Brownian Movement*(R. Fürth, ed.) Dover, New York (1959)]. MR**17:1035g****5.**N. Ikeda and S. Watanabe,*Stochastic Differential Equations and Diffusion Processes*, North-Holland Publishing Company, 1989. MR**90m:60069****6.**M. Kac,*On Some Connections between Probability Theory and Differential and Integral Equations*, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, 1951, pp. 189-215. MR**13:568b****7.**N.V. Krylov,*Controlled Diffusion Processes*, Springer-Verlag, 1980. MR**82a:60062****8.**D.W. Stroock and S.R.S. Varadhan,*Kiyosi Itô Selected Papers*(Stroock and Varadhan, eds.), Springer-Verlag, 1987. MR**88d:60001****9.**N. Wiener,*Differential Space*, J. Math. Phys.**2**(1923), 131-174.

Review Information:

Reviewer: Jin Ma

Affiliation: Purdue University

Email: majin@math.purdue.edu

Journal: Bull. Amer. Math. Soc.

**34**(1997), 49-53

MSC (1991): Primary 58G32, 60J60, 60J65; Secondary 35R60, 60G44, 60H15

DOI: https://doi.org/10.1090/S0273-0979-97-00697-6

Review copyright: © Copyright 1997 American Mathematical Society