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On solving integral equations using Markov chain Monte Carlo methods

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Doucet, Arnaud, Johansen, Adam M. and Tadić, Vladislav B.. (2010) On solving integral equations using Markov chain Monte Carlo methods. Applied Mathematics and Computation, Vol.216 (No.10). pp. 2869-2880. ISSN 0096-3003

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Official URL: http://dx.doi.org/10.1016/j.amc.2010.03.138

Abstract

In this paper, we propose an original approach to the solution of Fredholm equations of the second kind. We interpret the standard Von Neumann expansion of the solution as an expectation with respect to a probability distribution defined on a union of subspaces of variable dimension. Based on this representation, it is possible to use trans-dimensional Markov chain Monte Carlo (MCMC) methods such as Reversible Jump MCMC to approximate the solution numerically. This can be an attractive alternative to standard Sequential Importance Sampling (SIS) methods routinely used in this context. To motivate our approach, we sketch an application to value function estimation for a Markov decision process. Two computational examples are also provided.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Statistics

Library of Congress Subject Headings (LCSH):

Fredholm equations, Markov processes, Monte Carlo method

Journal or Publication Title:

Applied Mathematics and Computation

Publisher:

Elsevier Science Inc

ISSN:

0096-3003

Official Date:

15 July 2010

Dates:

Date	Event
15 July 2010	Published

Volume:

Vol.216

Number:

No.10

Number of Pages:

Page Range:

pp. 2869-2880

Identification Number:

10.1016/j.amc.2010.03.138

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

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