NUMERICAL SOLUTION OF FRACTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS AND STABILITY ANALYSIS

In this paper, we investigate the exponential mean square stability for both the solution of variable order fractional stochastic differential equations (FSDEs) with Poisson jump, as well for the compensated Milstein scheme implemented of the proposed model. First, we prove that the considered model has the property of exponential mean square stability. Moreover, it is shown that the compensated Milstein scheme can inherit the exponential mean square stability by using the variable order fractional stochastic differential equations with Poisson jump in the paper. Eventually, numerical solution are provided to show the effectiveness of the theoretical results. Also, by introducing the compensated Milstein scheme and by using some numerical integration technique as well approximating the integro part of the model by the simple trapezoidal rule, we obtain the same exponential mean square stability property for some restrictive stepsizes. Finally, we proved the exponential mean square stability by using the compensated Milstein method