Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix

Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix

This paper deals with the computation of invariant measures and stationary expectations for discrete-time Markov chains governed by a block-structured one-step transition probability matrix. The method generalizes in some respect Neuts’ matrix-geometric approach to vector-state Markov chains. The me...

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Main Authors: Hendrik Baumann, Thomas Hanschke
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2020/4318906
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spelling doaj-4058637ce3444a2bb4d3bb6c72c3769e2020-11-25T03:45:22ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422020-01-01202010.1155/2020/43189064318906Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition MatrixHendrik Baumann0Thomas Hanschke1Clausthal University of Technology, Institute of Mathematics, Erzstr. 1, 38678 Clausthal-Zellerfeld, GermanySimulation Science Center Clausthal-Göttingen, Arnold-Sommerfeld-Str. 6, 38678 Clausthal-Zellerfeld, GermanyThis paper deals with the computation of invariant measures and stationary expectations for discrete-time Markov chains governed by a block-structured one-step transition probability matrix. The method generalizes in some respect Neuts’ matrix-geometric approach to vector-state Markov chains. The method reveals a strong relationship between Markov chains and matrix continued fractions which can provide valuable information for mastering the growing complexity of real-world applications of large-scale grid systems and multidimensional level-dependent Markov models. The results obtained are extended to continuous-time Markov chains.http://dx.doi.org/10.1155/2020/4318906
collection DOAJ
language English
format Article
sources DOAJ
author Hendrik Baumann
Thomas Hanschke
spellingShingle Hendrik Baumann
Thomas Hanschke
Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix
Journal of Applied Mathematics
author_facet Hendrik Baumann
Thomas Hanschke
author_sort Hendrik Baumann
title Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix
title_short Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix
title_full Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix
title_fullStr Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix
title_full_unstemmed Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix
title_sort computation of invariant measures and stationary expectations for markov chains with block-band transition matrix
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2020-01-01
description This paper deals with the computation of invariant measures and stationary expectations for discrete-time Markov chains governed by a block-structured one-step transition probability matrix. The method generalizes in some respect Neuts’ matrix-geometric approach to vector-state Markov chains. The method reveals a strong relationship between Markov chains and matrix continued fractions which can provide valuable information for mastering the growing complexity of real-world applications of large-scale grid systems and multidimensional level-dependent Markov models. The results obtained are extended to continuous-time Markov chains.
url http://dx.doi.org/10.1155/2020/4318906
work_keys_str_mv AT hendrikbaumann computationofinvariantmeasuresandstationaryexpectationsformarkovchainswithblockbandtransitionmatrix
AT thomashanschke computationofinvariantmeasuresandstationaryexpectationsformarkovchainswithblockbandtransitionmatrix
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