Strong Convergence of Euler-Maruyama Schemes for McKean-Vlasov Stochastic Differential Equations under Local Lipschitz Conditions of State Variables

Strong Convergence of Euler-Maruyama Schemes for McKean-Vlasov Stochastic Differential Equations under Local Lipschitz Conditions of State Variables

At the invitation of Center for Mathematical Sciences, Professor Fuke Wu from Huazhong University of Science and Technologygave an online talk titled “Strong Convergence of Euler-Maruyama Schemes for McKean-Vlasov Stochastic Differential Equations under Local Lipschitz Conditions of State Variables” on Mar24th, 2021. Teachers and students in School of Mathematics and Physics in related research fields attended this academic colloquium.

This talk develops strong convergence of Euler-Maruyama (EM) schemes for approximating McKean-Vlasov stochastic differential equations (SDEs). In contrast to the existing work, a novel feature is the use of a much weaker condition-local Lipschitzian in the state variable. Existence and uniqueness of solutions of the original McKean-Vlasov SDE are established for obtaining the desired approximation by using an Euler-like sequence of interpolations and partition of the sample space. Then, the talk returns to the analysis of the EM scheme for approximating solutions of McKean-Vlasov SDEs. A strong convergence theorem is established. Moreover,the convergence rates under global conditions are obtained.