2008/11/17 by Elena Shmileva, Shmileva, Elena
Economics, Econometrics and Finance · Mathematics · #60G51 (Primary) 60G52 (Secondary) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G51 #msc:60G52
paper · pdf · doi:10.48550/arxiv.0811.2583
24 pages; just minor stylistic changes were made in this version
openalex publication_date 2008/11/17 · arxiv created 2009/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a symmetric α-stable Lévy process with α∈ (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.