A Multi-dimensional Linear Growth Birth and Death Process

Linear birth/immigration-death process with binomial catastrophes

In this paper, we study a birth/immigration-death processes under mild (binomial) catastrophes. We obtain explicit expressions for both the time-dependent (transient) and the limiting (equilibrium) factorial moments, which are then used to construct the transient and equilibrium distribution of the population size. We demonstrate that our approach is also applicable to multidimensional systems ...

A Birth-Death Process for Feature Allocation

We propose a Bayesian nonparametric prior over feature allocations for sequential data, the birthdeath feature allocation process (BDFP). The BDFP models the evolution of the feature allocation of a set of N objects across a covariate (e.g. time) by creating and deleting features. A BDFP is exchangeable, projective, stationary and reversible, and its equilibrium distribution is given by the Ind...

The Z-transform Applied to a Birth-death Process Having Varying Birth and Death Rates

The analysis of a birth-death process using the z-transform was recently reported for processes having fixed transition probabilities between states. The current report extends that analysis to processes having transition probabilities that can differ from state to state. It is then shown that the model can be used to study practical queuing and birth-death systems where the arrival, birth, ser...

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