On solving integral equations using Markov chain Monte Carlo methods

In this report, we propose an original approach to solve 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 de…ned on an 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. We sketch an application to value function estimation for a Markov decision process.