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arXiv · 1704.06521

Functional Erd\H{o}s-R\'enyi laws for L\'evy processes

Dimbihery Rabenoro
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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.

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Dimbihery Rabenoro. 2017-04-21. Functional Erd\H{o}s-R\'enyi laws for L\'evy processes. https://arxiv.org/abs/1704.06521

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