Minimal quasi-stationary distribution approximation for a birth and death process

Minimal quasi-stationary distribution approximation for a birth and death process

In a first part, we prove a Lyapunov-type criterion for the ξ1-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution. In a second part, we study the ergodicity and the convergence of a Fleming-Viot type particle system whose particles evolve independently as a birth and death process and jump on...

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

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

Sharp asymptotics for the quasi-stationary distribution of birth-and-death processes

We study a general class of birth-and-death processes with state space N that describes the size of a population going to extinction with probability one. This class contains the logistic case. The scale of the population is measured in terms of a 'carrying capacity' K. When K is large, the process is expected to stay close to its deterministic equilibrium during a long time but ultimately goes...

Quasi-stationary Distributions for Birth-death Processes with Killing

The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state (killing) is possible from any state rather than just one state. The purpose of this paper is to in...