OU-型Markov过程的单点击中概率与Range

HITTING PROBABILITIES OF SINGLE POINTS AND RANGE FOR MARKOV PROCESSES OF OU TYPE

摘要: 本文着重研究OU-型Markov过程的两个问题:第一,关于单点击中概率的问题,并在此基础上进一步确定OU型Markov过程局部时的存在性条件,这个问题的研究是受Kesten,H¹的影响,但本文中所用方法与1有本质的区别。第二,关于Range方面的问题,本文阐述了几类过程以概率1具有包含区间的Range。关于OU型Markov过程,Tokuzo,Shiga²研究了其常返性的判断准则,Sato,K³研究了其平稳分布,Hadjiev,D,I,⁵研究了其初遇问题,本文涉及的单点击中概率,局部时及Range尚没人研究过。

Abstract: In this paper we investigate two problems of Markov processes of OU type. One is its hitting probabilitis of single points and the results provide the existence of the local time for the processes. The other one is the range of the processes. We give several processes with range containning interval.