© 2013

Stochastic Differential Inclusions and Applications

  • Written by an award-winning expert in the field of Control Theory and Stochastic Processes

  • Presents new and original methods of solving select problems of optimal control theory and contains both solved problems and new open ones

  • Develops the theory of certain stochastic functional inclusions and its applications

  • May be treated as an introduction to a new approach to stochastic optimal control theory


Part of the Springer Optimization and Its Applications book series (SOIA, volume 80)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Michał Kisielewicz
    Pages 1-65
  3. Michał Kisielewicz
    Pages 67-102
  4. Michał Kisielewicz
    Pages 103-145
  5. Michał Kisielewicz
    Pages 147-179
  6. Michał Kisielewicz
    Pages 181-215
  7. Michał Kisielewicz
    Pages 217-252
  8. Michał Kisielewicz
    Pages 253-273
  9. Back Matter
    Pages 275-282

About this book


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.


Feynman-Kac formula partial differential inclusions set-valued stochastic integrals stochastic differential inclusions stochastic processes viability theory

Authors and affiliations

  1. 1., Faculty of MathematicsUniversity of Zielona GóraZielona GóraPoland

About the authors

Michał Kisielewicz is the author of over 70 articles on subjects including ordinary differential equations, systems theory, calculus of variations and optimal control, and probability theory and stochastic processes. He is a professor of mathematics at the University of Zielona Góra in Poland. In 2001, he was awarded the Order of Polonia Restituta, one of Poland's highest orders, for his achievements.

Bibliographic information


From the book reviews:

“In this monograph stochastic functional and differential inclusions with applications to stochastic optimal control are treated. … Each chapter contains a section of ‘Notes and Remarks’ with comments on related considerations available in the literature and some hints for further reading. … Readers with working knowledge in probability theory, stochastic processes, stochastic differential equations, and ordinary and partial differential equations will find a good presentation of the field of stochastic differential inclusions.” (Kurt Marti, Mathematical Reviews, June, 2014)