  For skew Brownian motion with two-valued drift, adopting a perturbation
approach we find expressions of its potential densities. As applications, we
recover its transition density and study its long-time asymptotic behaviors. We
also compare with previous results on transition densities for skew Brownian
motions. We propose two approaches for generating quasi-random samples by
approximating the cumulative distribution function and discussing their risk
measurement application.
