Duality for a class of continuous-time reversible Markov models

Using a conditional probability structure we build transition probabilities that drive appealing classes of reversible Markov processes. The mechanism used in such a construction allows to find a dual Markov process. This kind of duality is then used to compute the predictor operator of one process...

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Bibliographic Details
Published inStatistics (Berlin, DDR) Vol. 55; no. 1; pp. 231 - 242
Main Authors Palma, Freddy, Mena, Ramsés H.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2021
Taylor & Francis Ltd
Subjects
Conditional probability
Duality for Markov process
Markov chains
Markov processes
reversible Markov process
theory of queues
Transition probabilities
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Summary:Using a conditional probability structure we build transition probabilities that drive appealing classes of reversible Markov processes. The mechanism used in such a construction allows to find a dual Markov process. This kind of duality is then used to compute the predictor operator of one process via its dual. In particular, we identify the dual of some non-conjugate models, namely the queue model and a simple birth, death and immigration process. Such duals ensure that the computation of the predictor operators can be done via finite sums.
ISSN:0233-1888
1029-4910
DOI:10.1080/02331888.2021.1881098