TITLE:
The Arc-Sine Laws for the Skew Brownian Motion and Their Interpretation
AUTHORS:
Ivan H. Krykun
KEYWORDS:
Skew Brownian Motion, Local Time, Arc-Sine Law
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.2,
February
8,
2018
ABSTRACT: We consider the skew Brownian motion as a solution of some stochastic differential 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.