Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-23, 23 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-08-07
Country of Publication
Egypt
No. of Pages
23
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Baumann, Hendrik. 2020. Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes. Journal of Applied Mathematics،Vol. 2020, no. 2020, pp.1-23.
https://search.emarefa.net/detail/BIM-1174494
Modern Language Association (MLA)
Baumann, Hendrik. Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes. Journal of Applied Mathematics No. 2020 (2020), pp.1-23.
https://search.emarefa.net/detail/BIM-1174494
American Medical Association (AMA)
Baumann, Hendrik. Finite-State-Space Truncations for Infinite Quasi-Birth-Death Processes. Journal of Applied Mathematics. 2020. Vol. 2020, no. 2020, pp.1-23.
https://search.emarefa.net/detail/BIM-1174494
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174494