Caputo fractional stochastic differential equations: Lipschitz continuity in the fractional order

Abstract

In this paper, we consider a class of the Caputo fractional stochastic differential equations of fractional order $\hat{I}\pm \in (\frac{1}{2},1]$. Our aim is to analyze of the continuous dependence of solutions on the fractional order $\hat{I}\pm .$ We first provide explicit estimates for the rate of weak convergence the solutions. We then describe the exact asymptotic behavior of this convergence to show that the rate is optimal.

32 pages