Weak Convergence And Weak Stability Of Two Kinds Of Numerical Methods For A Class Of Stochastic Fractional Differential Equation With Multiplicative Noise

Based on the stochastic fractional differential equation with additive noise, this paper studied the weak convergence and weak stability of numerical methods for a class of stochastic fractional differential equation with multiplicative noise. Firstly,the numerical methods was constructed to solve the stochastic fractional differential equation with multiplicative noise, and then it was proved that the Euler method was weak convergence and weak stability when the fractional order a meets a ? (0, 1/2)and stochastic fractional differential equation satisfy some conditions. As same time,Taylor numerical method has similar conclusion. Finally, two numerical examples is given. The theoretical results are also confirmed by two numerical experiments.