Overview

This book is devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes. Interest is mainly confined to MCPs with Borel state and control spaces, and possibly unbounded costs. The book follows on from the authors earlier volume in this area, however, an important feature of the present volume is that it is essentially self-contained and can be read independently of the first volume, because although both volumes deal with similar classes of markov control processes the assumptions on the control models are usually different. This volume allows cost functions to take positive or negative values, as needed in some applications. 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.

Full Product Details

Author:   Onesimo Hernandez-Lerma ,  Jean B. Lasserre
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1999 ed.
Volume:   42
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.310kg
ISBN:  

9780387986944

ISBN 10:   0387986944
Pages:   277
Publication Date:   22 June 1999
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

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.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions