Onesimo Hernandez-Lerma, Jean B. Lasserre

Further Topics on Discrete-Time Markov Control Processes (eBook, PDF)

• Format: PDF

Produktbeschreibung

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. Although the book follows on from the author's earlier work, an important feature of this volume is that it is self-contained and can thus be read independently of the first. The control model studied is sufficiently general to include virtually all the usual discrete-time stochastic control models that appear in applications to engineering, economics, mathematical population processes, operations research, and management science.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 277
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461205616
• Artikelnr.: 44064185

Inhaltsangabe

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.