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Exponential convergence to a quasi-stationary distribution for birth–death processes with an entrance boundary at infinity
Published online by Cambridge University Press: 10 August 2022
Abstract
We study the quasi-stationary behavior of the birth–death process with an entrance boundary at infinity. We give by the h-transform an alternative and simpler proof for the exponential convergence of conditioned distributions to a unique quasi-stationary distribution in the total variation norm. In addition, we also show that starting from any initial distribution the conditional probability converges to the unique quasi-stationary distribution exponentially fast in the $\psi$ -norm.
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust