On Subexponential Convergence to Equilibrium of Markov Processes
Probability
2021-08-03 v2
Abstract
Studying the subexponential convergence towards equilibrium of a strong Markov process, we exhibit an intermediate Lyapunov condition equivalent to the control of some moment of a hitting time. This provides a link, similar (although more intricate) to the one existing in the exponential case, between the coupling method and the approach based on the existence of a Lyapunov function for the generator, in the context of the subexponential rates found by Fort-Roberts (2005), Douc-Fort-Guillin (2009) and Hairer (2016).
Keywords
Cite
@article{arxiv.2004.12826,
title = {On Subexponential Convergence to Equilibrium of Markov Processes},
author = {Armand Bernou},
journal= {arXiv preprint arXiv:2004.12826},
year = {2021}
}
Comments
22 pages. Slightly strengthened the main result, added some comparisons with previous results and added some examples