Friedman A. Stochastic Differential Equations and Applications. Vol. 1

Качество: текстовый слой, электронное оглавлениеAcademic Press, 1975. — 244 p. — ISBN: 0122682017The object of this book is to develop the theory of systems of stochastic differential equations and then give applications in probability, partial differential equations and stochastic control problems.
In Volume 1 we develop the basic theory of stochastic differential equations and give a few selected topics. Volume 2 will be devoted entirely to applications.
Chapters 1-5 form the basic theory of stochastic differential equations. The material can be found in one form or another also in other texts.
Chapter 6 gives connections between solutions of partial differential equations and stochastic differential equations. The material in partial differential equations is essentially self-contained; for some of the proofs the reader is referred to an appropriate text.
In Chapter 7 Girsanov’s formula is established. This formula is becoming increasingly useful in the theory of stochastic control.
In Chapters 8 and 9 we study the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity.
The book is written in a textlike style, namely, the material is essentially self-contained and problems are given at the end of each chapter. The only prerequisite is elementary probability; more specifically, the reader is assumed to be familiar with concepts such as conditional expectation, independence, and with elementary facts such as the Borel-Cantelli lemma. This prerequisite material can be found in any probability text, such as Breiman [1; Chapters 3,4].