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General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

  • Book
  • © 2014

Overview

Authors:
  1. Qi Lü

    1. School of Mathematics, Sichuan University, Chengdu, China

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    You can also search for this author in PubMed   Google Scholar

  2. Xu Zhang

    1. School of Mathematics, Sichuan University, Chengdu, China

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • First monograph on Pontryagin-type maximum principle for stochastic evolution equations
  • Provides useful approach to the topic, useful for both beginners and experts
  • Provides detailed proof for most of results faced in the book
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Qi Lü, Xu Zhang
    Pages 1-9

  3. Preliminaries

    • Qi Lü, Xu Zhang
    Pages 11-22

  4. Well-Posedness of the Vector-Valued BSEEs

    • Qi Lü, Xu Zhang
    Pages 23-35

  5. Well-Posedness Result for the Operator-Valued BSEEs with Special Data

    • Qi Lü, Xu Zhang
    Pages 37-47

  6. Sequential Banach-Alaoglu-Type Theorems in the Operator Version

    • Qi Lü, Xu Zhang
    Pages 49-59

  7. Well-Posedness of the Operator-Valued BSEEs in the General Case

    • Qi Lü, Xu Zhang
    Pages 61-89

  8. Some Properties of the Relaxed Transposition Solutions to the Operator-Valued BSEEs

    • Qi Lü, Xu Zhang
    Pages 91-107

  9. Necessary Condition for Optimal Controls, the Case of Convex Control Domains

    • Qi Lü, Xu Zhang
    Pages 109-113

  10. Necessary Condition for Optimal Controls, the Case of Non-convex Control Domains

    • Qi Lü, Xu Zhang
    Pages 115-144

  11. Back Matter

    Pages 145-146
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Keywords

About this book

The classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagin type maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.

Authors and Affiliations

  • School of Mathematics, Sichuan University, Chengdu, China

    Qi Lü, Xu Zhang

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