I will present a joint work with Quentin Berger and Loïc Bethencourt. We study the asymptotic of the probability that a signed additive functional of a recurrent one-dimensional diffusion stays below some constant level for a long time. Under our hypothesis we prove that this persistence probability decreases polynomially and we find the persistence exponent. For that we decompose the diffusion into excursions and the problem is reduced to study the fluctuations  of some Lévy process naturally associated with the additive functional.
org: CAPUTO Pietro