Markov Chains and Stochastic Stability

Markov Chains and Stochastic Stability by Sean P. Meyn, Richard L. Tweedie.

Markov Chains and Stochastic Stability is part of the Communications and Control Engineering Series (CCES) edited by Professors B.W. Dickinson, E.D. Sontag, M. Thoma, A. Fettweis, J.L. Massey and J.W. Modestino. The area of Markov chain theory and application has matured over the past 20 years into...

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Bibliographic Details
Main Authors: Meyn, Sean P. (Author), Tweedie, Richard L. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: London : Springer London : Imprint: Springer, 1993.
Edition:1st ed. 1993.
Series:Communications and Control Engineering,
Springer eBook Collection.
Subjects:
Applied mathematics.
Engineering mathematics.
Electrical engineering.
Control engineering.
Robotics.
Mechatronics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I Communication and Regeneration
  • 1 Heuristics
  • 2 Markov Models
  • 3 Transition Probabilities
  • 4 Irreducibility
  • 5 Pseudo-atoms
  • 6 Topology and Continuity
  • 7 The Nonlinear State Space Model
  • II Stability Structures
  • 8 Transience and Recurrence
  • 9 Harris and Topological Recurrence
  • 10 The Existence of ?
  • 11 Drift and Regularity
  • 12 Invariance and Tightness
  • III Convergence
  • 13 Ergodicity
  • 14 ƒ-Ergodicity and ƒ-Regularity
  • 15 Geometric Ergodicity
  • 16 V-Uniform Ergodicity
  • 17 Sample Paths and Limit Theorems
  • 18 Positivity
  • 19 Generalized Classification Criteria
  • IV Appendices
  • A Mud Maps
  • A.l Recurrence versus transience
  • A.2 Positivity versus nullity
  • A.3 Convergence Properties
  • B Testing for Stability
  • B.l A Glossary of Drift Conditions
  • B.2 The scalar SETAR Model: a complete classification
  • C A Glossary of Model Assumptions.
  • C.l Regenerative Models
  • C.2 State Space Models
  • D Some Mathematical Background
  • D.l Some Measure Theory
  • D.2 Some Probability Theory
  • D.3 Some Topology
  • D.4 Some Real Analysis
  • D.5 Some Convergence Concepts for Measures
  • D.6 Some Martingale Theory
  • D.7 Some Results on Sequences and Numbers
  • References
  • Symbols Index.

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