$L^p(\Omega)$-Difference of One-Dimensional Stochastic Differential Equations with Discontinuous Drift

Abstract

We consider a one-dimensional stochastic differential equations (SDE) with irregular coefficients. The purpose of this paper is to estimate the $L^p(\Omega)$-difference of SDEs using the norm of the difference of coefficients, where the discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is bounded, uniformly elliptic and H\"older continuous. As an application, we consider the stability problem.