Quasi-Birth-and-Death processes with an Infinite phase space

Abstract:

A quasi-birth-and-death process (QBD) is a two-dimensional Markov chain for which the transition matrix has a block tridiagonal structure, and is a widely studied stochastic model used in, for example, telecommunications traffic modelling. The first variable of the QBD process is called the level, the second variable the phase. The properties of QBDs with finitely many possible values of the phase variable have been studied extensively. In particular the level process of a positive-recurrent QBD with finitely many phases has a stationary distribution which decays geometrically. The situation is more complicated for a QBD process with countably many possible values of the phase. In this talk we present results for the stationary distribution of QBDs with infinitely many phases and the convergence of phase-truncation schemes.

About the speaker: Allan Motyer is currently a research fellow at the Prince of Wales Clinical School, University of New SouthWales, studying statistical methods for analysis of large genomic data sets. This seminar is based on work from his PhD at the University of Melbourne.