Discrete-Time Markov Control Processes

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 Stochastic Kernels.- Appendix D Multifunctions and Selectors.- Appendix E Convergence of Probability Measures.- References.