Quasi-birth-and-death processes, level-geometric distributions. An aggregation/disaggregation approach
The author considers a special class of homogeneous continuous time Markov chains with block tridiagonal infinitesimal generators, called quasi-birth and death Markov chains. He describes a functional analytic approach to the study of such Markov chains. This approach provides not only a clear analytic interpretation of the concepts introduced elsewhere using probabilistic ideas but also provides suitable basis for computations. An iterative aggregation/disaggregation method is proposed to solve the problem if the quasi-birth and death Markov chain possess a level-geometric stationary distribution.
iterative aggregation/disaggregation method
scientific article; zbMATH DE number 1912273