学术报告（张希承 5.24）

摘要 ：We propose a full discretization scheme for linear/nonlinear (McKean-Vlasov) SDEs driven by Brownian motions or $\alpha$-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 study a functional CLT for the approximation of ODEs and the convergence of invariant measures for SDEs. As a practical application, we construct a compound Poisson approximation for 2D-Navier Stokes equations on torus and show the optimal convergence rate.