On Subexponential Convergence to Equilibrium of Markov Processes
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).
Type
Publication
Séminaire de Probabilités LI
This article was part of my PhD thesis. One can find it as Chapter 5 of the volume LI of the “Séminaire de Probabilités”.
