Perturbed Markov Chains with Damping Component

Dmitrii Silvestrov (), Sergei Silvestrov, Benard Abola, Pitos Seleka Biganda, Christopher Engström, John Magero Mango and Godwin Kakuba
Additional contact information
Dmitrii Silvestrov: Stockholm University
Sergei Silvestrov: Mälardalen University
Benard Abola: Mälardalen University
Pitos Seleka Biganda: Mälardalen University
Christopher Engström: Mälardalen University
John Magero Mango: Makerere University
Godwin Kakuba: Makerere University

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 1, 369-397

Abstract: Abstract The paper is devoted to studies of regularly and singularly perturbed Markov chains with damping component. In such models, a matrix of transition probabilities is regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We perform a detailed perturbation analysis for such Markov chains, particularly, give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, explicit coupling type upper bounds for the rate of convergence in ergodic theorems for n-step transition probabilities, as well as ergodic theorems in triangular array mode.

Keywords: Markov chain; Damping component; Information network; Regular perturbation; Singular perturbation; Stationary distribution; Asymptotic expansion; Rate of convergence; Coupling; Ergodic theorem; Triangular array mode; 60J10; 60J22; 65C40; 90B15; 68M11 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-020-09815-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-020-09815-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-020-09815-9

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().