The Excursion Structure Of One-dimension Diffusion Process And The Uniqueness Of The Martingale Problems

In this paper, we main to study the excursion structure of one-dimension Diffusion process and the uniqueness of the martingales problems. One-dimension Diffusion process is usually to be defined as the continuous-path strong Markov process. It is the Markov process which has the most completely structure. depicted the structure of one-dimension Diffusion process in analytic ways. Now we use the excursion theory to analysis this problem again, we also calculate the resolvent and generator in every condition. So we depicted the structure of one-dimension Diffusion process in probability ways. On the other hand, we disguss the uniqueness of the weak solution to the martingale problem in the sense of probability.