A stability result for stochastic differential equations driven by fractional Brownian motions (Q1929674)

Summary: We study the stability of the solutions of stochastic differential equations driven by fractional Brownian motions with Hurst parameter greater than \(1/2\). We prove that, when the initial conditions, the drift, and the diffusion coefficients as well as the fractional Brownian motions converge in a suitable sense, then the sequence of the solutions of the corresponding equations converge in Hölder norm to the solution of a stochastic differential equation. The limit equation is driven by the limit fractional Brownian motion and its coefficients are the limits of the sequence of the coefficients.