Some Study On Occupation Time Of Diffusion Process

The occupation time is an attractive topic in the research of stochastic process recently,it means the amount of time a stochastic process spends in a certain region,it has many applications in the research of risk theory and financial models.Based on the recent research,we adopt the Poisson approach of Li and Zhou(2104)to further study the occupation time of diffusion process.This thesis is divided into three chapters.The first chapter is an introduction of the research background and current situation.We then outline the main results of this thesis.In the second chapter we find the Laplace transform of occupation time over finite interval(0,a)for diffusion process before an independent exponential time eq,such as At the end of this chapter,we apply these results to find explicit expressions for the examples of Brownian motion and Brownian motion with drift.In the third chapter we find the joint Laplace transform of occupation times over semi-infinite intervals(-?,a)and(a,?)for diffusion process before an independent exponential time eq,such as And then we apply these results to find explicit expressions for the examples of Brow-nian motion and Brownian motion with drift.