This book presents the second part of a two-volume series devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes. As in Volume I (AM 30 Discrete-Time Markov Control Processes: Basic Optimality Criteria), interest is mainly confined to MCPs with Borel state and control spaces. However, an important feature of the present volume is that is it essentially self-contained and can be read independently of Volume I, because the assumptions on the control models are usually different.

Zusammenfassung
Devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes, the text is mainly confined to MCPs with Borel state and control spaces.

Inhalt
7 Ergodicity and Poisson's Equation.- 7.1 Introduction.- 7.2 Weighted norms and signed kernels.- 7.3 Recurrence concepts.- 7.4 Examples on w-geometric ergodicity.- 7.5 Poisson's equation.- 8 Discounted Dynamic Programming with Weighted Norms.- 8.1 Introduction.- 8.2 The control model and control policies.- 8.3 The optimality equation.- 8.4 Further analysis of value iteration.- 8.5 The weakly continuous case.- 8.6 Examples.- 8.7 Further remarks.- 9 The Expected Total Cost Criterion.- 9.1 Introduction.- 9.2 Preliminaries.- 9.3 The expected total cost.- 9.4 Occupation measures.- 9.5 The optimality equation.- 9.6 The transient case.- 10 Undiscounted Cost Criteria.- 10.1 Introduction.- 10.2 Preliminaries.- 10.3 From AC-optimality to undiscounted criteria.- 10.4 Proof of Theorem 10.3.1.- 10.5 Proof of Theorem 10.3.6.- 10.6 Proof of Theorem 10.3.7.- 10.7 Proof of Theorem 10.3.10.- 10.8 Proof of Theorem 10.3.11.- 10.9 Examples.- 11 Sample Path Average Cost.- 11.1 Introduction.- 11.2 Preliminaries.- 11.3 The w-geometrically ergodic case.- 11.4 Strictly unbounded costs.- 11.5 Examples.- 12 The Linear Programming Approach.- 12.1 Introduction.- 12.2 Preliminaries.- 12.3 Linear programs for the AC problem.- 12.4 Approximating sequences and strong duality.- 12.5 Finite LP approximations.- 12.6 Proof of Theorems 12.5.3, 12.5.5, 12.5.7.- References.- Abbreviations.- Glossary of notation.