Quasi-stationary distribution for the Langevin process in cylindrical domains, part II: overdamped limit

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 proce...

Stationary Distribution of a Perturbed Quasi-birth-and-death Process

Quasi-Stationary Simulation: the Subcritical Contact Process

We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of the process fall into the absorbing state before the quasi-stationary regime is attained. With relatively modest simulations, the method yields an estimate o...

Quasi-stationary simulation of the contact process

We review a recently devised Monte Carlo simulation method for the direct study of quasi-stationary properties of stochastic processes with an absorbing state. The method is used to determine the static correlation function and the interparticle gap-length distribution in the critical one-dimensional contact process. We also find evidence for power-law decay of the interparticle distance distri...

Domain of attraction of the quasi-stationary distribution for the linear birth and death process

Article history: Received 14 October 2010 Available online 14 July 2011 Submitted by M. Peligrad