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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Series: | Journal of Applied Mathematics |
Online Access: | http://dx.doi.org/10.1155/2020/4318906 |
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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 |
_version_ |
1715124466135072768 |