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arXiv · 2104.06027

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

Loïc Béthencourt
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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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Loïc Béthencourt. 2021-04-13. Stable limit theorems for additive functionals of one-dimensional diffusion processes. https://arxiv.org/abs/2104.06027

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