超Ornstein Uhlenbeck过程的一个占位时性质

An Occupation Time Property of Super OrnsteinUhlenbeck Processes

讨论了Rd上底过程是暂留Ornstein-Uhlenbeck过程的测度值分支马尔可夫过程,考虑了其占位时过程的一个性质,证明了对任意的底空间的维数d,过程在任意一个波莱尔有界子集上花去的总占位时是有限的结论,结合超布朗运动对应的结果,发现了不同的底过程所对应的超过程的性质有时是截然不同的。

In this paper, we consider measurevalued branching Markov processes with underlying transient OrnsteinUhlenbeck processes on Rd and investigate a property of the corresponding weighted occupation time processes. We prove that for any underlying dimension d, the processes spend a finite total weighted occupation time in any bounded Borel subset of Rd. Comparing the result with that of super Brownian motion we find that the properties of superprocesses corresponding to different underlying processes are semetime quite different.