Markov Chains and Stochastic Stability (Communications and Control Engineering) （Edition.）

Meyn, Sean P./ Tweedie, Richard L.

Springer-Verlag Berlin and Heidelberg GmbH & Co. K（1993/06発売）

• 製本 Hardcover:ハードカバー版／ページ数 566 p.
• 言語 ENG
• 商品コード 9783540198321
• DDC分類 519.233

Full Description

The area of Markov chain theory and application has matured over the past 20 years. This publication deals with the action of Markov chains on general state spaces. It discusses the theories and the use to be gained, concentrating on the areas of engineering, operations research and control theory. Throughout, the theme of stochastic stability and the search for practical methods of verifying such stability, provide a new and powerful technique which not only affects applications, but also the development of the theory itself. The impact of the theory on specific models is discussed in detail.

Contents

Contents: Communication and Regeneration: Heuristics.- Markov Models.- Transition Probabilities.- Irreducibility.- Pseudo-atoms.- Topology and Continuity.- Nonlinear State Space Model.- Stability Structures: Transience and Recurrence.- Harris and Topological Recurrence.- The Existence of +.- Drift and Regularity.- Invariance and Tightness. Convergence: Ergodicity.- f-Ergodicity and f-Regularity.- Geometric Ergodicity.- V-Uniform Ergodicity.- Sample Paths and Limit Theorems.- Positivity.- Generalised Classification Criteria. Appendices: Mud Maps.- Testing for Stability.- Glossary of Model Assumptions.- Mathematical Background.