A Sharp Error Estimate Of Euler-Maruyama Method For Stochastic Volterra Integral Equations

In this paper,the Euler-Maruyama method is used to solve a class of nonlin-ear stochastic Volterra integral equations,which can be derived from stochastic frac-tional substantial integro-dierential equations.The existence and uniqueness of the solution are proved for the nonlinear stochastic Volterra integral equations under the non-Lipschitz condition.Moreover,the sharp convergence estimate with(?)(hα+1/2)ifα∈(0,1/2),(?)(h·(?))if α=1/2 and(?)(h)if a ∈(1/2,1],respectively,are established for the nonlinear stochastic Volterra integral equations,which can be revised and sup-plemented theory results of our recent work[26].In particular,it also closes a gap that was left the convergence analysis in[31].Finally,numerical experiments are given to illustrate the effectiveness of the presented methods.