广义随机Volterra积分微分方程的截断Euler-Maruyama方法的强收敛性

Strong convergence of the truncated Euler-Maruyama method for generalized stochastic Volterra integro-differential equations

运用截断Euler-Maruyama(EM)方法研究了广义随机Volterra积分微分方程的强收敛性.首先,在局部Lipschitz条件和Khasminskii型条件下证明了截断EM数值解的p阶矩有界性和强收敛性;其次,在较强的假设条件下讨论了截断EM数值解的收敛率;最后通过数值例子验证理论结果的可行性和有效性.

In this paper,the strong convergence of the numerical solutions for generalized stochastic Volterra integro-differential equations is studied by the truncated Euler-Maruyama(EM)method.Firstly,under local Lipschitz condition and the Khasminskii-type condition,we prove the p th moment boundedness and strong convergence of the truncated EM method of the numerical solutions.Furthermore,under some stronger assumptions,the convergence rate of the truncated EM method of the numerical solutions is discussed.Finally,a numerical example is given to illustrate the feasibility and validity of our theoretical results.