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 $\alpha \in (0,2]$.

Cited by in corpus (1)

• Persistence problems for additive functionals of one-dimensional Markov processes