Stable limit theorems for additive functionals of one-dimensional diffusion processes

2021/04/13 by Loïc Béthencourt, Béthencourt, Loïc
Computer Science · Mathematics · #60F05 #60J60 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · doi:10.48550/arxiv.2104.06027

openalex publication_date 2021/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some explicit conditions on the additive functional so that its fluctuations behave like some α-stable process in large time for α∈(0,2].

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