一类扩散过程轨道的excursion分解

THE EXCURSION DECOMPOSITION OF THE PATHS OF A CLASS OF DIFFUSIONS

  • 摘要: 本文对于一类扩散过程的轨道作了excursion分解。应用Maisonnenve给出的exitsystem,得到了通过扩散的转移密度表出的相应泊松点过程的特征测度。作为例子,给出了Ornstein-Uhlenbeek过程的一个随机积分表示,最后用Geoor的方法计算出了熟知的该过程的一个不变测度。

     

    Abstract: In this paper, the excursion decomposition of the paths of a cerlain class of diffusions is carried out. Using Maisonneuve’s exit system, we obtain the concrete form of the characteristic measure n of the respective Poisson point processes in terms of the transition density functions of the diffusions. As an example, we give a stochastic integral version of Ornstein-Uhlenbeck Processes starting from zero. Finally, although it is known, an invariant measure of these processes is obtained via Getoor’s method.

     

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