Uniform convergence of conditional distributions for absorbed one-dimensional diffusions - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Advances in Applied Probability Year : 2018

Uniform convergence of conditional distributions for absorbed one-dimensional diffusions

Abstract

This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusions. We obtain a necessary and sufficient condition for the exponential convergence to a unique quasi-stationary distribution in total variation, uniformly with respect to the initial distribution. Our approach is based on probabilistic and coupling methods, contrary to the classical approach based on spectral theory results. We provide several conditions ensuring this criterion, which apply to most practical cases. As a by-product, we prove that most strict local martingale diffusions are strict in a stronger sense: their expectation at any given positive time is actually uniformly bounded with respect to the initial position. We provide several examples and extensions, including the sticky Brownian motion and some one-dimensional processes with jumps. We also give exponential ergodicity results on the Q-process.
Fichier principal
Vignette du fichier
article_without_killing_1d_v2.pdf (248.95 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01166960 , version 1 (20-05-2016)

Licence

Attribution

Identifiers

Cite

Nicolas Champagnat, Denis Villemonais. Uniform convergence of conditional distributions for absorbed one-dimensional diffusions. Advances in Applied Probability, 2018, 50 (1), pp.178-203. ⟨10.1017/apr.2018.9⟩. ⟨hal-01166960⟩
183 View
111 Download

Altmetric

Share

Gmail Facebook X LinkedIn More