A Stationary Drake Equation Distribution as a Balance of Birth-death Processes

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

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...

A Note on Quasi-stationary Distributions of Birth-death Processes and the Sis Logistic Epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco [4] studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Φ on the space of probability distributions on {1, 2, . . .}. In the case of a birth-death process, one ca...

Quasi - Birth - Death Processes

1 Description of the Model This case study is analog to the one described in [2]. We considered a system consisting of a fixed number of m processors and an infinite queue for storing job requests. The processing speed of a processor is described by the rate γ, while λ describes the incoming rate of new jobs. If a new job arrives while at least one processor is idle, the job will be processed d...