The Arc-Sine Laws for the Skew Brownian Motion and Their Interpretation

Abstract

We consider the skew Brownian motion as a solution of some stochastic dif ferential equation. We prove for the skew Brownian motion the analogues of the arc-sine laws for Wiener process. Unlike of existing results, we are forced to consider a stochastic differential equation with discontinuous diffusion coefficient. Possible interpretations of obtained results are suggested.