Functional Erd\H{o}s-R\'enyi laws for L\'evy processes
Statistics Theory
2025-09-23 v7 Statistics Theory
Abstract
In this paper we establish functional Erd\H{o}s-Renyi laws for L\'evy processes, i.e. limit theorems for sets of functions on [0,1] associated to their increments. First, we determine precise conditions under which, in a general framework, such a convergence is derived from a large deviations principle for probability measures induced by the sample paths of such a process. Then, by checking that these conditions are fulfilled, we obtain, under two usual assumptions on exponential moments, such limit theorems from well-known large deviations principles.
Keywords
Cite
@article{arxiv.1704.06521,
title = {Functional Erd\H{o}s-R\'enyi laws for L\'evy processes},
author = {Dimbihery Rabenoro},
journal= {arXiv preprint arXiv:1704.06521},
year = {2025}
}