Work

A Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations

Year: 2000

Type: article

Abstract: Perturbations to Markov chains and Markov processes are considered. The unperturbed problem is assumed to be geometrically ergodic in the sense usually established through the use of Foster--Lyapunov drift conditions. The perturbations are assumed to be uniform, in a weak sense, on bounded time intervals. The long-time behavior of the perturbed chain is studied. Applications are given to numerical approximations of a randomly impulsed ODE, an Itô stochastic differential equation (SDE), and a parabolic stochastic partial differential equation (SPDE) subject to space-time Brownian noise. Existing perturbation theories for geometrically ergodic Markov chains are not readily applicable to these situations since they require very stringent hypotheses on the perturbations.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/s0036142998337235

Authors: T. Shardlow, A. M. Stuart

Institutions: Engineering and Physical Sciences Research Council, California Institute of Technology, University of Warwick

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

OpenAlex ID: W2021270935

FWCI: 1.876

Cites: 35

Cited by: 60

Related to: 10