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Stochastic Differential Inclusions and Applications

  • Book
  • © 2013

Overview

Authors:
  1. Michał Kisielewicz

    1. , Faculty of Mathematics, University of Zielona Góra, Zielona Góra, Poland

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  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Stochastic Processes

    • Michał Kisielewicz
    Pages 1-65

  3. Set-Valued Stochastic Processes

    • Michał Kisielewicz
    Pages 67-102

  4. Set-Valued Stochastic Integrals

    • Michał Kisielewicz
    Pages 103-145

  5. Stochastic Differential Inclusions

    • Michał Kisielewicz
    Pages 147-179

  6. Viability Theory

    • Michał Kisielewicz
    Pages 181-215

  7. Partial Differential Inclusions

    • Michał Kisielewicz
    Pages 217-252

  8. Stochastic Optimal Control Problems

    • Michał Kisielewicz
    Pages 253-273

  9. Back Matter

    Pages 275-282
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Keywords

About this book

​This book aims to further develop the theory of stochastic functional inclusions and their applications for describing the solutions of the initial and boundary value problems for partial differential inclusions. The self-contained volume is designed to  introduce the reader in a systematic fashion, to new methods of the stochastic optimal control theory from the very beginning. 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 work is divided into seven chapters, with the first two acting as an introduction, containing selected material dealing with point- and set-valued stochastic processes, and the final two devoted to applications and optimal control problems. The book presents recent and pressing issues in stochastic processes, control, differential games, optimization and their application in finance, manufacturing, queueing networks, and climate control. 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.

Reviews

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)

Authors and Affiliations

  • , Faculty of Mathematics, University of Zielona Góra, Zielona Góra, Poland

    Michał Kisielewicz

About the author

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.

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