A note on strong solutions of stochastic differential equations with a discontinuous drift coefficient

Abstract

The existence of a mean-square continuous strong solution is established for vector-valued Itô stochastic differential equations with a discontinuous drift coefficient, which is an increasing function, and with a Lipschitz continuous diffusion coefficient. A scalar stochastic differential equation with the Heaviside function as its drift coefficient is considered as an example. Upper and lower solutions are used in the proof.