A Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations
- Creators
- Shardlow, T.
-
Stuart, A. M.
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.
Additional Information
© 2000 Society for Industrial and Applied Mathematics. Received by the editors April 13, 1998; accepted for publication (in revised form) September 16, 1998; published electronically March 23, 2000. Supported by the National Science Foundation under grant DMS-95-04879. We thank Peter Baxendale, Peter Glynn James Norris, and Neil O'Connell for helpful discussions and also the referees for a number of valuable comments.Attached Files
Published - s0036142998337235.pdf
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Additional details
- Eprint ID
- 78141
- Resolver ID
- CaltechAUTHORS:20170613-080747440
- DMS-95-04879
- NSF
- Created
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2017-06-13Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Other Numbering System Name
- Andrew Stuart
- Other Numbering System Identifier
- J45