双曲空间上超布朗运动的范围

The Range of Super-Brownian Motions on Hyperbolic Space

对双曲空间上的超布朗运动进行了研究,证明了该过程的范围属于某集合的概率可以表示为一个奇异边值问题的解．在得到了这个解的一个极限结果以后,给出了上述概率的一个渐近行为．对于维数d≥2,还证明了从黎曼测度出发的超过程在任何内点非空的有界Borel子集上的占位时是无穷的结论．

The author investigates a super-Brownian motion on a hyperbolic space and shows that the probability of the event that the range of the superprocess is within a certain set can be expressed by a solution of a singular boundary valued problem. After obtaining a limit result of the solution, he gives an asymptotic behavior of the probability. The author also proves that the superprocess, starting from the Riemannian measure, spends an infinite total weighted occupation time in any bounded Borel subset with non-empty interior whenever dimension d ≥ 2.