Sum rules for hitting times of Markov chains

José Luis Palacios; José M. Renom

doi:10.1016/j.laa.2010.03.014

Sum rules for hitting times of Markov chains

José Luis Palacios
, José M. Renom

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Using matrix algebra we obtain a general equation for the sum, normalized with suitable constants, of all the expected hitting times in an ergodic Markov chain. This equation yields as corollaries, among others, Broder and Karlin's formula, Foster's nth formula and an expression of the Kirchhoff index in terms of the eigenvalues of the Laplacian.

Original language	English
Pages (from-to)	491-497
Number of pages	7
Journal	Linear Algebra and Its Applications
Volume	433
Issue number	2
DOIs	https://doi.org/10.1016/j.laa.2010.03.014
State	Published - 1 Aug 2010
Externally published	Yes

Keywords

Fundamental matrix
Hitting times
Kirchhoff index

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10.1016/j.laa.2010.03.014

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title = "Sum rules for hitting times of Markov chains",

abstract = "Using matrix algebra we obtain a general equation for the sum, normalized with suitable constants, of all the expected hitting times in an ergodic Markov chain. This equation yields as corollaries, among others, Broder and Karlin's formula, Foster's nth formula and an expression of the Kirchhoff index in terms of the eigenvalues of the Laplacian.",

keywords = "Fundamental matrix, Hitting times, Kirchhoff index",

author = "Palacios, \{Jos{\'e} Luis\} and Renom, \{Jos{\'e} M.\}",

year = "2010",

month = aug,

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doi = "10.1016/j.laa.2010.03.014",

language = "English",

volume = "433",

pages = "491--497",

journal = "Linear Algebra and Its Applications",

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TY - JOUR

T1 - Sum rules for hitting times of Markov chains

AU - Palacios, José Luis

AU - Renom, José M.

PY - 2010/8/1

Y1 - 2010/8/1

N2 - Using matrix algebra we obtain a general equation for the sum, normalized with suitable constants, of all the expected hitting times in an ergodic Markov chain. This equation yields as corollaries, among others, Broder and Karlin's formula, Foster's nth formula and an expression of the Kirchhoff index in terms of the eigenvalues of the Laplacian.

AB - Using matrix algebra we obtain a general equation for the sum, normalized with suitable constants, of all the expected hitting times in an ergodic Markov chain. This equation yields as corollaries, among others, Broder and Karlin's formula, Foster's nth formula and an expression of the Kirchhoff index in terms of the eigenvalues of the Laplacian.

KW - Fundamental matrix

KW - Hitting times

KW - Kirchhoff index

UR - https://www.scopus.com/pages/publications/77953301079

U2 - 10.1016/j.laa.2010.03.014

DO - 10.1016/j.laa.2010.03.014

M3 - Article

AN - SCOPUS:77953301079

SN - 0024-3795

VL - 433

SP - 491

EP - 497

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2

ER -

Sum rules for hitting times of Markov chains

Abstract

Keywords

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