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

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 $\alpha$-stable process in large time for $\alpha\in(0,2]$.
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https://hal.inria.fr/hal-03197696
Contributor : Loïc Béthencourt <>
Submitted on : Wednesday, April 14, 2021 - 9:59:59 AM
Last modification on : Friday, April 16, 2021 - 3:28:42 AM

### Identifiers

• HAL Id : hal-03197696, version 1
• ARXIV : 2104.06027

### Citation

Loïc Béthencourt. Stable limit theorems for additive functionals of one-dimensional diffusion processes. 2021. ⟨hal-03197696⟩

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