The first Laurent series coefficients for singularly perturbed stochastic matrices

Konstantin E. Avrachenkov; Moshe Haviv

doi:10.1016/j.laa.2003.12.047

The first Laurent series coefficients for singularly perturbed stochastic matrices

Konstantin E. Avrachenkov^*, Moshe Haviv

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Conference article › peer-review

11 Scopus citations

Abstract

There are a few procedures for computing the Laurent series expansions for the mean passage time matrix and for the deviation matrix of a singularly perturbed Markov chain. We suggest here a method for computing the first terms in these expansions in a way which highlights the system dynamics in various time scales.

Original language	English
Pages (from-to)	243-259
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	386
Issue number	1-3 SUPPL.
DOIs	https://doi.org/10.1016/j.laa.2003.12.047
State	Published - 15 Jul 2004
Event	Conference on the Numerical Solution of MC - Urbana-Champaign, IL, United States Duration: 3 Sep 2003 → 5 Sep 2003

Keywords

Aggregation/disaggregation
Deviation matrix
Laurent series
Markov chains
Mean first passage times
Singular perturbations

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10.1016/j.laa.2003.12.047

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title = "The first Laurent series coefficients for singularly perturbed stochastic matrices",

abstract = "There are a few procedures for computing the Laurent series expansions for the mean passage time matrix and for the deviation matrix of a singularly perturbed Markov chain. We suggest here a method for computing the first terms in these expansions in a way which highlights the system dynamics in various time scales.",

keywords = "Aggregation/disaggregation, Deviation matrix, Laurent series, Markov chains, Mean first passage times, Singular perturbations",

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AU - Avrachenkov, Konstantin E.

AU - Haviv, Moshe

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N2 - There are a few procedures for computing the Laurent series expansions for the mean passage time matrix and for the deviation matrix of a singularly perturbed Markov chain. We suggest here a method for computing the first terms in these expansions in a way which highlights the system dynamics in various time scales.

AB - There are a few procedures for computing the Laurent series expansions for the mean passage time matrix and for the deviation matrix of a singularly perturbed Markov chain. We suggest here a method for computing the first terms in these expansions in a way which highlights the system dynamics in various time scales.

KW - Aggregation/disaggregation

KW - Deviation matrix

KW - Laurent series

KW - Markov chains

KW - Mean first passage times

KW - Singular perturbations

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3 SUPPL.

T2 - Conference on the Numerical Solution of MC

Y2 - 3 September 2003 through 5 September 2003

ER -

The first Laurent series coefficients for singularly perturbed stochastic matrices

Abstract

Keywords

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