各向同性Lévy过程的球的不可避免集合
Unavodiable collections of balls for isotropic Lévy processes
摘要：
欧几里得空间$\R^d$中成对不相交球的集合$\{\bar{B}(x_n,r_n)\}_{n\ge 1}$被称为相对于瞬态过程$X$是可避免的，如果该过程具有正概率逃逸到无穷大而不击中任何球。本文研究了单峰各向同性Lévy过程满足一定标度假设的可避免性的充分条件和必要条件。这些条件用过程的特征指数表示，或者用相应的格林函数表示。我们也讨论了同样的问题的一个随机收集的球。所得结果推广了布朗运动情形的几个近期结果。
英文摘要：
A collection $\{\bar{B}(x_n,r_n)\}_{n\ge 1}$ of pairwise disjoint balls in the Euclidean space $\R^d$ is said to be avoidable with respect to a transient process $X$ if the process with positive probability escapes to infinity without hitting any ball. In this paper we study sufficient and necessary conditions for avoidability with respect to unimodal isotropic Lévy processes satisfying a certain scaling hypothesis. These conditions are expressed in terms of the characteristic exponent of the process, or alternatively, in terms of the corresponding Green function. We also discuss the same problem for a random collection of balls. The results are generalization of several recent results for the case of Brownian motion.
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