Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes
For dealing numerically with the infinite-state-space Markov chains, a truncation of the state space is inevitable, that is, an approximation by a finite-state-space Markov chain has to be performed. In this paper, we consider level-dependent quasi-birth-death processes, and we focus on the computat...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/2678374 |
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| author | Hendrik Baumann |
| author_facet | Hendrik Baumann |
| author_sort | Hendrik Baumann |
| collection | DOAJ |
| description | For dealing numerically with the infinite-state-space Markov chains, a truncation of the state space is inevitable, that is, an approximation by a finite-state-space Markov chain has to be performed. In this paper, we consider level-dependent quasi-birth-death processes, and we focus on the computation of stationary expectations. In previous literature, efficient methods for computing approximations to these characteristics have been suggested and established. These methods rely on truncating the process at some level N, and for N⟶∞, convergence of the approximation to the desired characteristic is guaranteed. This paper’s main goal is to quantify the speed of convergence. Under the assumption of an f-modulated drift condition, we derive terms for a lower bound and an upper bound on stationary expectations which converge quickly to the same value and which can be efficiently computed. |
| format | Article |
| id | doaj-art-8b2b8b68670e481d9266fb6530e19638 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8b2b8b68670e481d9266fb6530e196382025-02-03T06:46:40ZengWileyJournal of Applied Mathematics1110-757X1687-00422020-01-01202010.1155/2020/26783742678374Finite-State-Space Truncations for Infinite Quasi-Birth-Death ProcessesHendrik Baumann0Clausthal University of Technology, Institute of Mathematics, Erzstr. 1, 38678 Clausthal-Zellerfeld, GermanyFor dealing numerically with the infinite-state-space Markov chains, a truncation of the state space is inevitable, that is, an approximation by a finite-state-space Markov chain has to be performed. In this paper, we consider level-dependent quasi-birth-death processes, and we focus on the computation of stationary expectations. In previous literature, efficient methods for computing approximations to these characteristics have been suggested and established. These methods rely on truncating the process at some level N, and for N⟶∞, convergence of the approximation to the desired characteristic is guaranteed. This paper’s main goal is to quantify the speed of convergence. Under the assumption of an f-modulated drift condition, we derive terms for a lower bound and an upper bound on stationary expectations which converge quickly to the same value and which can be efficiently computed.http://dx.doi.org/10.1155/2020/2678374 |
| spellingShingle | Hendrik Baumann Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes Journal of Applied Mathematics |
| title | Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes |
| title_full | Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes |
| title_fullStr | Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes |
| title_full_unstemmed | Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes |
| title_short | Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes |
| title_sort | finite state space truncations for infinite quasi birth death processes |
| url | http://dx.doi.org/10.1155/2020/2678374 |
| work_keys_str_mv | AT hendrikbaumann finitestatespacetruncationsforinfinitequasibirthdeathprocesses |