Uniform convergence of penalized time-inhomogeneous Markov processes

TL;DR

This paper establishes a general criterion for exponential convergence of penalized time-inhomogeneous Markov processes, with applications to diffusion processes conditioned on avoiding zero and to birth-death processes in random environments.

Contribution

It introduces a novel sufficient condition for exponential contraction of Feynman-Kac semi-groups in penalized, time-inhomogeneous Markov processes.

Findings

Exponential contraction criterion proven for specific processes

Application to diffusion processes conditioned on avoiding zero

Application to birth-death processes in random environments

Abstract

We provide an original and general sufficient criterion ensuring the exponential contraction of Feynman-Kac semi-groups of penalized processes. This criterion is applied to time-inhomogeneous one-dimensional diffusion processes conditioned not to hit 0 and to penalized birth and death processes evolving in a quenched random environment.