Matrix Analysis for Continuous-Time Markov Chains
Continuous-time Markov chains have transition matrices that vary continuously in time. Classical theory of nonnegative matrices, M-matrices and matrix exponentials is used in the literature to study their dynamics, probability distributions and other stochastic properties. For the benefit of Perron-...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-12-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2021-0157 |
| _version_ | 1811222937110315008 |
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| author | Le Hung V. Tsatsomeros M. J. |
| author_facet | Le Hung V. Tsatsomeros M. J. |
| author_sort | Le Hung V. |
| collection | DOAJ |
| description | Continuous-time Markov chains have transition matrices that vary continuously in time. Classical theory of nonnegative matrices, M-matrices and matrix exponentials is used in the literature to study their dynamics, probability distributions and other stochastic properties. For the benefit of Perron-Frobenius cognoscentes, this theory is surveyed and further adapted to study continuous-time Markov chains on finite state spaces. |
| first_indexed | 2024-04-12T08:23:18Z |
| format | Article |
| id | doaj.art-a43a387ea5724b458af040795c70ffa8 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-04-12T08:23:18Z |
| publishDate | 2021-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-a43a387ea5724b458af040795c70ffa82022-12-22T03:40:28ZengDe GruyterSpecial Matrices2300-74512021-12-0110121923310.1515/spma-2021-0157Matrix Analysis for Continuous-Time Markov ChainsLe Hung V.0Tsatsomeros M. J.1Mathematics and Statistics, Washington State University, Pullman, WA 99164Mathematics and Statistics, Washington State University, Pullman, WA 99164Continuous-time Markov chains have transition matrices that vary continuously in time. Classical theory of nonnegative matrices, M-matrices and matrix exponentials is used in the literature to study their dynamics, probability distributions and other stochastic properties. For the benefit of Perron-Frobenius cognoscentes, this theory is surveyed and further adapted to study continuous-time Markov chains on finite state spaces.https://doi.org/10.1515/spma-2021-0157continuous-time markov chainstochastic matrixm-matrixmatrix exponentialexponential nonnegativityirreducible matrixprimitive matrixgroup inverse15b5115a4815a1815a0960j1092d40 |
| spellingShingle | Le Hung V. Tsatsomeros M. J. Matrix Analysis for Continuous-Time Markov Chains Special Matrices continuous-time markov chain stochastic matrix m-matrix matrix exponential exponential nonnegativity irreducible matrix primitive matrix group inverse 15b51 15a48 15a18 15a09 60j10 92d40 |
| title | Matrix Analysis for Continuous-Time Markov Chains |
| title_full | Matrix Analysis for Continuous-Time Markov Chains |
| title_fullStr | Matrix Analysis for Continuous-Time Markov Chains |
| title_full_unstemmed | Matrix Analysis for Continuous-Time Markov Chains |
| title_short | Matrix Analysis for Continuous-Time Markov Chains |
| title_sort | matrix analysis for continuous time markov chains |
| topic | continuous-time markov chain stochastic matrix m-matrix matrix exponential exponential nonnegativity irreducible matrix primitive matrix group inverse 15b51 15a48 15a18 15a09 60j10 92d40 |
| url | https://doi.org/10.1515/spma-2021-0157 |
| work_keys_str_mv | AT lehungv matrixanalysisforcontinuoustimemarkovchains AT tsatsomerosmj matrixanalysisforcontinuoustimemarkovchains |