Stochastic Differential Equations for Applications

The report contains a systematic and concise exposition of stochastic differential equations. The author's attention is focused on a presentation which gives a necessary insight into the mathematical structure of the contemporary theory as well as into the most efficient methods of applying and solving stochastic differential equations.

The presentation starts with a sort description of physical and engineering problems whose modelling leads to stochastic differential equations. Chapters I and II contain the concepts and results of the stochastic process theory (Ch. I) and the stochastic calculus (continuity, differentiation and integration of stochastic processes (Ch. II)). This material constitutes a mathematical basis for the formulation and analysis of stochastic differential equations.

Chapters III and IV are devoted to the main subject of the textbook. In Chapter III the most important mathematical results associated with stochastic differential equations and their interpretations are given. This material forms a basis for the development of practical methods of solving different classes of stochastic equations which are presented systematically in Chapter IV.

The references provided in the end of each chapter constitute an introduction to very recent achievements both in theory and applications of stochastic differential equations in various engineering (especially mechanical) problems.