Stability Problem for One-Dimensional Stochastic Differential Equations with Discontinuous Drift

Abstract

We consider one-dimensional stochastic differential equations (SDEs) with irregular coefficients. The goal of this paper is to estimate the L p (Ω)-difference between two SDEs using a norm associated to the difference of coefficients. In our setting, the (possibly) discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is bounded, uniformly elliptic and Holder continuous. As an application of this result, we consider the stability problem for this class of SDEs.