Strong convergence of Euler–Maruyama schemes for McKean–Vlasov stochastic differential equations under local Lipschitz conditions of state variables

Abstract This paper develops strong convergence of the Euler–Maruyama (EM) schemes for approximating McKean–Vlasov stochastic differential equations (SDEs). In contrast to existing work, a novel feature is use much weaker condition—local Lipschitzian in state variable, but under uniform linear growth assumption. To obtain desired approximation, first establishes existence and uniqueness solutions original SDE using Euler-like sequence interpolations partition sample space. Then, returns analysis EM scheme SDEs. A theorem established. Moreover, rates global conditions are obtained.