Author(s)

Ivan H. Krykun^1,2

¹Pervomajs’k Branch of Admiral Makarov National Shipbuilding University, Pervomajs’k, Ukraine.
²Institute of Applied Mathematics and Mechanics of NAS of Ukraine, Slovjans’k, Ukraine.

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.

Skew Brownian Motion, Local Time, Arc-Sine Law

Krykun, I. (2018) The Arc-Sine Laws for the Skew Brownian Motion and Their Interpretation. Journal of Applied Mathematics and Physics, 6, 347-357. doi: 10.4236/jamp.2018.62033.