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Explicit solutions for a general class of Markov processes
Author(s) -
van Leeuwaarden Johan S.H.,
Squillante Mark S.,
Winands Erik M.M.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700857
Subject(s) - class (philosophy) , probabilistic logic , bernoulli's principle , markov chain , hypergeometric distribution , mathematics , matrix (chemical analysis) , markov process , hypergeometric function , pure mathematics , algebra over a field , computer science , statistics , physics , artificial intelligence , materials science , composite material , thermodynamics
We derive explicit solutions for the matrix‐geometric stationary distribution (and related measures) of a general class of infinite multidimensional Markov processes based on the probabilistic interpretations of the fundamental solution matrices and Bernoulli excursions, leading to explicit expressions for these matrix elements in terms of hypergeometric functions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)