This research monograph is the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including the treatment of the intricate measure-theoretic issues.
Author(s): Dimitri P. Bertsekas and Steven E. Shreve (Eds.)
Series: Mathematics in Science and Engineering 139
Edition: 1
Publisher: Elsevier, Academic Press
Year: 1978
Language: English
Pages: iii-xiii, 1-323
Content:
Edited by
Page iii
Copyright page
Page iv
Dedication
Page v
Preface
Pages xi-xii
Acknowledgments
Page xiii
Chapter 1 Introduction
Pages 1-21
Part I: Analysis of Dynamic Programming Models
Page 23
Chapter 2 Monotone Mappings Underlying Dynamic Programming Models
Pages 25-38
Chapter 3 Finite Horizon Models
Pages 39-51
Chapter 4 Infinite Horizon Models under a Contraction Assumption
Pages 52-69
Chapter 5 Infinite Horizon Models under Monotonicity Assumptions
Pages 70-90
Chapter 6 A Generalized Abstract Dynamic Programming Model
Pages 91-98
Part II: Stochastic Optimal Control Theory
Page 99
Chapter 7 Borel Spaces and Their Probability Measures
Pages 101-187
Chapter 8 The Finite Horizon Borel Model
Pages 188-212
Chapter 9 The Infinite Horizon Borel Models
Pages 213-241
Chapter 10 The Imperfect State Information Model
Pages 242-265
Chapter 11 Miscellaneous
Pages 266-272
Appendix A The Outer Integral
Pages 273-281
Appendix B Additional Measurability Properties of Borel Spaces
Pages 282-302
Appendix C The Hausdorff Metric and the Exponential Topology
Pages 303-311
References
Pages 312-315
Table of Propositions, Lemmas, Definitions, and Assumptions
Pages 317-320
Index
Pages 321-323
