Euler Approximation for Non-Autonomous Mixed Stochastic Differential Equations in Besov Norm

Abstract

We consider a kind of non-autonomous mixed stochastic differential equations driven by standard Brownian motions and fractional Brownian motions with Hurst index $H ∈ (1/2, 1)$. In the sense of stochastic Besov norm with index $γ$, we prove that the rate of convergence for Euler approximation is $O(δ^{2H−2γ})$, here $δ$ is the mesh of the partition of $[0, T]$.