Exponential convergence to quasi-stationary distribution and Q-process
نویسندگان
چکیده
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, infinitedimensional population models with Brownian mutations and neutron transport dynamics absorbed at the boundary of a bounded domain.
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