A Lyapunov Bound for Solutions of Poisson's Equation

Abstract

Suppose that X is a positive recurrent Harris chain with invariant measure pi. We develop a Lyapunov function criterion that permits one to bound the solution g to Poisson's equation for X. This bound is then applied to obtain sufficient conditions that guarantee that the solution be an element of L sub p (pi). When p = 2, the square integrability of g implies the validity of a functional central limit theorem for the Markov chain. We illustrate the technique with applications to the waiting time sequence of the single-server queue and autoregressive sequences. Keywords: Functional central limit theorem.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1989
Accession Number
ADA220223

Entities

People

  • Peter W. Glynn

Organizations

  • Stanford University

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Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Guarantees
  • Lyapunov Functions
  • Markov Chains
  • Markov Processes
  • Mathematics
  • Military Research
  • New York
  • Operations Research
  • Probability
  • Sequences
  • Stochastic Processes
  • Theorems
  • United States
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Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Mathematical Modeling and Probability Theory.