Explicit Numerical Approximations For Mc Kean-Vlasov Stochastic Differential Equations

The coefficients of McKean-Vlasov stochastic differential equation depend on the current solution distribution(MV-SDE).Combining particle method and truncated Euler-Maruyama(EM)developed recently,this paper investigates the numerical method of MV-SDE that drift coefficient satisfies super-linear growth condition.Firstly,an interacting particle system as well as propagation of chaos which means the strong convergence of the particle system for corresponding MV-SDE are introduced.Then,in addition to the construction of numerical scheme to approximate the interacting particle system,the strong convergence is studied.Furthermore,as a result of propagation of chaos,the strong convergence result of numerical solution to the original MV-SDE is provided.Finally,through the example and numerical simulations,the conclusions obtained in this paper are verified.