Compound Poisson particle approximation for McKean-Vlasov SDEs

06/12/2023

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by   Xicheng Zhang, et al.

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We propose a full discretization scheme for linear/nonlinear (McKean-Vlasov) SDEs driven by Brownian motions or α-stable processes by means of the compound Poisson particle approximations. The advantage of the scheme is that it simultaneously discretizes the time and space variables for McKean-Vlasov SDEs, and the approximation processes can be devised as a Markov chain with values in lattice. In particular, we show the propagation of chaos under quite weak assumptions on the coefficients, including those with polynomial growth. Additionally, we also study a functional CLT for the approximation of ODEs and the convergence of invariant measures for linear SDEs. As a practical application, we construct a compound Poisson approximation for 2D-Navier Stokes equations on torus and show the optimal convergence rate.