Uniform convergence of penalized time-inhomogeneous Markov processes

Nicolas Champagnat (1, 2) , Denis Villemonais (1, 2)

1 TOSCA - TO Simulate and CAlibrate stochastic models
2 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: penalized processes; birth and death processes in random environment with killing; Dobrushin's ergodic coefficient; one-dimensional diffusions with absorption; uniform exponential mixing; Feynman-Kac formula; asymptotic stability; time-inhomogeneous Markov processes

Domaines: Probabilités [math.PR]

Nicolas Champagnat, Denis Villemonais. Uniform convergence of penalized time-inhomogeneous Markov processes. ESAIM: Probability and Statistics, 2018, 22, pp.129-162. ⟨10.1051/ps/2017022⟩. ⟨hal-01290222⟩