对称α稳态过程驱动的随机微分方程数值分析

Numerical analysis for stochastic differential equations driven by symmetric α-stable process

研究了一类对称α稳态过程驱动的随机微分方程数值解问题.这类随机微分方程的漂移项具有超线性增长系数.采用半隐式Euler-Maruyama算法得到:对于任意小的ε>0和α∈[1,2),其数值解强收敛率是α-ε4.

In this paper,the numerical solution of a class of stochastic differential equations driven by symmetricα-stable process is studied.The drift coefficient of stochastic differential equations under consideration is allowed to grow super-linearly.The strong convergence of numerical solution by the semi-implicit Euler-Maruyama algorithm is shown with the rate ofα-ε4 for arbitrarily smallε>0 andα∈[1,2).