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Friday, March 1, 2019

**Abstract:** In this talk, I discuss the computational problem of approximating the solution of a probability weighted Poisson equation, in terms of finite number of particles sampled from the probability distribution. The poisson equation arises in the theory of nonlinear filtering and optimal transportation. I present an approximation procedure based on the stochastic viewpoint of the problem. Then, I present the error analysis of the approximation using the Lyapunov stability theory in stochastic analysis.