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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  
Dates: 


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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