2017/04/21 by Dimbihery Rabenoro, Rabenoro, Dimbihery
Economics, Econometrics and Finance · Physics and Astronomy · #60F10 #60F15 #60F17 #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #FOS: Mathematics #Statistics Theory (math.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1704.06521
openalex publication_date 2017/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we establish functional Erdős-Renyi laws for Lévy 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.