Stochastic Differential Inclusions and Applications [electronic resource] / by Michał Kisielewicz.

Preface -- List of Symbols -- 1. Stochastic Processes -- 2. Set-Valued Stochastic Processes -- 3. Set-Valued Stochastic Intergrals -- 4. Stochastic Differential Inclusions -- 5.Viability Theory -- 6. Partial Differential Inclusions -- 7. Some Optimal Control Problems -- Bibliography -- Subject Index.

Stochastic Differential Inclusions and Applications further develops the theory of stochastic functional inclusions and their applications. This self-contained volume is designed to systematically introduce the reader from the very beginning to new methods of the stochastic optimal control theory. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The text presents recent and pressing issues in stochastic processes, control, differential games, and optimization that can be applied to finance, manufacturing, queueing networks, and climate control. The work is divided into seven chapters, with the first two, containing selected introductory material dealing with point- and set-valued stochastic processes. The final two chapters are devoted to applications and optimal control problems. Written by an award-winning author in the field of stochastic differential inclusions and their application to control theory, this book is intended for students and researchers in mathematics and applications, particularly those studying optimal control theory. It is also highly relevant for students of economics and engineering. The book can also be used as a reference on stochastic differential inclusions. Knowledge of select topics in analysis and probability theory are required.