对称α-稳定过程的移位小偏差和Chung LIL
Shifted small deviations and Chung LIL for symmetric alpha-stable processes
摘要：
考虑对称$α$ -稳定Lévy过程，其参数为$α\in (1,2)$ .当移位函数是从0开始的任意连续函数时，我们研究了在一致拓扑中这些过程的移位小球概率。我们得到这些概率的确切下降率，包括常数。利用这些小球估计，我们得到了吸引函数连续的$α$ -稳定Lévy过程的泛函LIL.在某些选择的正规化函数下，重正化$α$稳定Lévy过程族的极限集等于$[0,1]$上所有从0开始的连续函数的集合。
英文摘要：
Consider a symmetric $α$-stable Lévy process with $α\in (1,2)$. We study shifted small ball probabilities for these processes in the uniform topology, when the shift function is an arbitrary continuous function which starts at 0. We obtain the exact rate of decrease for these probabilities including constants. Using these small ball estimates, we obtain a functional LIL for $α$-stable Lévy process with attracting functions that are continuous. It occurs that the limit set for the family of renormalized $α$-stable Lévy processes is equal to the set of all continuous functions on $[0,1]$ which start at 0, under certain choice of normalizing functions.
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