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**Stochastic differential equations. An introduction with applications.
6th ed.**
*(English)*
Zbl 1025.60026

Universitext. Berlin: Springer. xxiii, 360 p. (2003).

This is now the sixth edition of the excellent book on stochastic differential equations and related topics. [The earlier editions (1985, 1989, 1992, 1995, 1998) are covered by Zbl 0567.60055, Zbl 0694.60046, Zbl 0747.60052, Zbl 0841.60037 and Zbl 0897.60056, respectively.]

The author presents and explains with complete proofs essential material on stochastic differential equations (with respect to Brownian motion) and diffusion processes; in addition the text covers applications to population growth models, linear filtering, optimal stopping, stochastic optimal control, the Dirichlet and Poisson problem for partial differential equations and mathematical finance. The popularity of the book may very well be based on the fact that the presentation is successfully balanced between being easily accessible for a broad audience and being mathematically rigorous. The book is a first choice for courses at graduate level in applied stochastic differential equations. The inclusion of detailed solutions to many of the exercises in this edition also makes it very useful for self-study.

The author presents and explains with complete proofs essential material on stochastic differential equations (with respect to Brownian motion) and diffusion processes; in addition the text covers applications to population growth models, linear filtering, optimal stopping, stochastic optimal control, the Dirichlet and Poisson problem for partial differential equations and mathematical finance. The popularity of the book may very well be based on the fact that the presentation is successfully balanced between being easily accessible for a broad audience and being mathematically rigorous. The book is a first choice for courses at graduate level in applied stochastic differential equations. The inclusion of detailed solutions to many of the exercises in this edition also makes it very useful for self-study.

Reviewer: Evelyn Buckwar (Berlin)

### MSC:

60Hxx | Stochastic analysis |

60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |

60G35 | Signal detection and filtering (aspects of stochastic processes) |