Uniform convergence of penalized time-inhomogeneous Markov processes
  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. 
Nicolas Champagnat (TOSCA), Denis Villemonais (TOSCA)
math.PR