The analysis and property of two classes of skew Markov processes

Abstract

The skew diffusion process is a special diffusion process. The stochastic differential equation expression of such a special process contains the symmetric local time.Due to its special property, this model is widely used in physics and biology. Starting from skew Brownian motion,this work summaries its two constructions: discrete approximation and jointly probability distribution. Based on the skew Brownian motion, we provide the definitions for the skew Ornstein-Uhlenbeck (OU) process and skew branching process, and derive their properties: transition density, first hitting time, etc.We also introduce some applications under the skew diffusion processes.