Discrete-Time Markov Control Processes: Basic Optimality Criteria / Edition 1 available in Hardcover
- Pub. Date:
- Springer New York
This book provides a unified, comprehensive treatment of some recent theoretical developments on Markov control processes. Interest is mainly confined to MCPs with Borel state and control spaces, and possibly unbounded costs and non-compact control constraint sets. The control model studied is sufficiently general to include virtually all the usual discrete-time shastic control models that appear in applications to engineering, economics, mathematical population processes, operations research, and management science. Much of the material appears for the first time in book form.
Table of Contents
1 Introduction and Summary.- 1.1 Introduction.- 1.2 Markov control processes.- 1.3 Preliminary examples.- 1.4 Summary of the following chapters.- 2 Markov Control Processes.- 2.1 Introduction.- 2.2 Markov control processes.- 2.3 Markov policies and the Markov property.- 3 Finite-Horizon Problems.- 3.1 Introduction.- 3.2 Dynamic programming.- 3.3 The measurable selection condition.- 3.4 Variants of the DP equation.- 3.5 LQ problems.- 3.6 A consumption-investment problem.- 3.7 An inventory-production system.- 4 Infinite-Horizon Discounted-Cost Problems.- 4.1 Introduction.- 4.2 The discounted-cost optimality equation.- 4.3 Complements to the DCOE.- 4.4 Policy iteration and other approximations.- 4.5 Further optimality criteria.- 4.6 Asymptotic discount optimality.- 4.7 The discounted LQ problem.- 4.8 Concluding remarks.- 5 Long-Run Average-Cost Problems.- 5.1 Introduction.- 5.2 Canonical triplets.- 5.3 The vanishing discount approach.- 5.4 The average-cost optimality inequality.- 5.5 The average-cost optimality equation.- 5.6 Value iteration.- 5.7 Other optimality results.- 5.8 Concluding remarks.- 6 The Linear Programming Formulation.- 6.1 Introduction.- 6.2 Infinite-dimensional linear programming.- 6.3 Discounted cost.- 6.4 Average cost: preliminaries.- 6.5 Average cost: solvability.- 6.6 Further remarks.- Appendix A Miscellaneous Results.- Appendix B Conditional Expectation.- Appendix C Shastic Kernels.- Appendix D Multifunctions and Selectors.- Appendix E Convergence of Probability Measures.- References.