THE RUNNING MAXIMUM OF A LEVEL-DEPENDENT QUASI-BIRTH-DEATH PROCESS

Level-Dependent Quasi-Birth-and-Death Processes

This article defines and describes the level-dependent quasi-birth-and-death (LDQBD) process, a generalization of the homogeneous (or level-independent) quasi-birth-and-death (QBD) process. Like its level-independent counterpart, the LDQBD process is a bivariate Markov process whose transition probability matrix (or infinitesimal generator matrix) exhibits a block tri-diagonal structure. Howeve...

Numerical solution of level dependent quasi-birth-and-death processes

We consider the numerical computation of stationary distributions for level dependent quasi-birth-and-death processes. An algorithm based on matrix continued fractions is presented and compared to standard solution techniques. Its computational efficiency and numerical stability is demonstrated by numerical examples.

Quasistationary Distributions for Level-dependent Quasi-birth-and-death Processes

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

Maximum Likelihood Estimation in the Birth-and-death Process By