A Wavelet-Based Computational Framework for a Block-Structured Markov Chain with a Continuous Phase Variable

We consider the computing issues of steady probabilities for block-structured discrete-time Markov chains that are upper-Hessenberg or lower-Hessenberg transition kernels with a continuous phase set. An effective computational framework is proposed based on wavelet transform, which extends and modifies arguments in literature quasi-birth-death (QBD) processes. A numerical procedure developed fast discrete several examples presented to illustrate its effectiveness.