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Numerical integration using V-uniformly ergodic Markov chains

Part of: Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

Peter Mathé
Peter Mathé*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics
*
∗ Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany. Email address: mathe@wias-berlin.de
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Abstract

We study numerical integration based on Markov chains. Our focus is on establishing error bounds uniformly on classes of integrands. Since in general state space the concept of uniform ergodicity is too restrictive to cover important cases, we analyze the error of V-uniformly ergodic Markov chains. We place emphasis on the interplay between ergodicity properties of the transition kernel, the initial distributions and the classes of integrands. Our analysis is based on arguments from interpolation theory.

Keywords

Numerical integrationV-uniformly ergodic Markov chaininterpolation

MSC classification

Primary: 65C05: Monte Carlo methods
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1104 - 1112
Copyright
Copyright © Applied Probability Trust 2004 

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