a stochastic algorithm to solve multiple dimensional fredholm integral equations of the second kind

in the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional fredholm integral equations of the second kind‎. ‎the solution of the‎ integral equation is described by the neumann series expansion‎. ‎each term of this expansion can be considered as an expectation which is approximated by a continuous markov chain monte carlo method‎. ‎an algorithm is proposed to simulate a continuous markov chain with probability density function arisen from an importance sampling technique‎. ‎theoretical results are established in a normed space to justify the convergence of the proposed method‎. ‎the method has a simple structure and it is a good candidate for parallelization because of the fact that many independent sample paths are used to estimate the solution‎. ‎numerical results are performed in order to confirm the efficiency and accuracy of the present work‎.