Stochastic differential equations. An introduction with applications. 3rd ed. (English) Zbl 0747.60052

Universitext. Berlin etc.: Springer-Verlag. xiii, 224 p. (1992).
[For the first edition (1985) see Zbl 0567.60055, for the second one (1989) see Zbl 0694.60046.]
Øksendal’s book is a very popular introduction to stochastic differential equations for applied mathematicians, engineers and scientists. Besides basic material on stochastic differential equations (with respect to Brownian motion) and diffusion processes the text covers applications to population growth models, linear filtering, optimal stopping, stochastic optimal control, and the Dirichlet and Poisson problem for partial differential equations. For this third edition exercises have been included for each chapter, ranging from routine problems to somewhat more challenging ones — a good mixture for use as a textbook on an introductory graduate level. The addition of exercises and the fact that the book is now typeset in TEX, making reading much easier, should make this text a first choice for courses in applied stochastic differential equations.
Reviewer: W.Kliemann (Ames)


60Hxx Stochastic analysis
60J60 Diffusion processes
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
93E20 Optimal stochastic control
60G35 Signal detection and filtering (aspects of stochastic processes)