The Maximum And Minimum Excursions Of Symmtrical Markov Process

In this paper we investigate the excursion of an elliptic diffusion process on R~d(d ≥3).Using the basic formula of potential, we generalize the corresponding results of the first hitting time of Brownian motion .We utilize the strong Markov property to obtain moderate estimates for the distributions of the minimum excursion and three maximum excursions: before the first hitting time, before the last exit time and from the first hitting to the last exit.This thesis consists of three chapters .In chapter one , the distributions of the last exit time and the corresponding results of Brownian motion in Markov process are introduced ,and previous remarkable achievements on the excursion of Brownian motion are numerated too ,also ,we introduce the main results and the history of elliptic diffusion process; In chapter two ,we summarily describe the excursion in Markov process and the result of the first hitting time of the elliptic diffusion process ; In last chapter ,we study estimates for the distributions of above three maximum excursions and minimum excursion in the elliptic diffusion process on R (d≥3), which leads the excursion of Brownian motion on ball on R (d≥3) to become a particular case .