Continuous dependence of solutions of stochastic differential equations driven by standard and fractional Brownian motion on a parameter (Q2890725)

A one-dimensional stochastic differential equation driven by both a standard Brownian motion and a fractional Brownian motion with Hurst parameter \(H\in(1/2,1)\) is considered. The coefficients of the equation are assumed to be nonhomogeneous. The coefficients as well as the random initial condition \(X_0^u\) depend on a certain parameter \(u\in[0,u_0]\). Assuming that \(X_0^u\) converges in probability to \(X_0^0\), conditions on the coefficients as functions of the parameter are found under which the solutions \(\{X_t^u,t\in[0,T]\}\) converge to \(\{X_t^0,t\in[0,T]\}\) uniformly in probability as \(u\rightarrow 0\).