On stable numerical approximation for non autonomous stochastic differential equations with H¨older continuous diffusion coefficient

Abstract

   This paper discusses a numerical approximation for time depedent stochastic differential equation with H¨older continuous diffusion coefficient. We introduce a new approximation scheme and study its convergence in L1-norm. An important feature of the new scheme is that it preserves the exponential stability as well as the non-negativity of the exact solution.