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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. 28692880. ISSN 00963003

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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 transdimensional 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:  00963003 
Official Date:  15 July 2010 
Volume:  Vol.216 
Number:  No.10 
Number of Pages:  12 
Page Range:  pp. 28692880 
Identification Number:  10.1016/j.amc.2010.03.138 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
References:  [1] D. P. Bertsekas, Dynamic Programmming and Optimal Control, Athena 
URI:  http://wrap.warwick.ac.uk/id/eprint/5735 
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