Author | Hernรกndez-Lerma, Onรฉsimo. author |
---|---|
Title | Further Topics on Discrete-Time Markov Control Processes [electronic resource] / by Onรฉsimo Hernรกndez-Lerma, Jean Bernard Lasserre |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1999 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0561-6 |
Descript | XIII, 277 p. online resource |
7 Ergodicity and Poissonโs Equation -- 7.1 Introduction -- 7.2 Weighted norms and signed kernels -- 7.3 Recurrence concepts -- 7.4 Examples on w-geometric ergodicity -- 7.5 Poissonโs 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