An overview of some stochastic stability methods

Serguei Foss, Panagiotis Takis Konstantopoulos

Research output: Contribution to journalLiterature review

75 Citations (Scopus)

Abstract

This paper presents an overview of stochastic stability methods, mostly motivated by (but not limited to) stochastic network applications. We work with stochastic recursive sequences, and, in particular, Markov chains in a general Polish state space. We discuss, and frequently compare, methods based on (i) Lyapunov functions, (ii) fluid limits, (iii) explicit coupling (renovating events and Harris chains), and (iv) monotonicity. We also discuss existence of stationary solutions and instability methods. The paper focuses on methods and uses examples only to exemplify the theory. Proofs are given insofar as they contain some new, unpublished, elements, or are necessary for the logical reading of this exposition.

Original languageEnglish
Pages (from-to)275-303
Number of pages29
JournalJournal of the Operations Research Society of Japan
Volume47
Issue number4
Publication statusPublished - Dec 2004

Keywords

  • Applied probability
  • Coupling
  • Ergodicity
  • Harris chains
  • Lyapunov functions
  • Markov chains
  • Stability
  • Stationary processes
  • Stochastic networks
  • Stochastic recursive sequences

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