Exponential convergence to quasi-stationary distribution and Q-process
  For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the $Q$-process (the process conditioned to never be absorbed). We apply these results to one-dimensional birth and death processes with catastrophes, multi-dimensional birth and death processes, infinite-dimensional population models with Brownian mutations and neutron transport dynamics absorbed at the boundary of a bounded domain. 
Nicolas Champagnat (INRIA Sophia Antipolis / INRIA Nancy - Grand Est/   IECN, IECL), Denis Villemonais (INRIA Sophia Antipol...
math.PR