Upper escape rate of Markov chains on weighted graphs

Xueping Huang; Yuichi Shiozawa

doi:10.1016/j.spa.2013.08.004

Upper escape rate of Markov chains on weighted graphs

Xueping Huang, Yuichi Shiozawa

Graduate School of Natural Science and Technology

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

11 Citations (Scopus)

Abstract

We obtain an upper escape rate function for a continuous time minimal symmetric Markov chain defined on a locally finite weighted graph. This upper rate function, which has the same form as the manifold setting, is given in terms of the volume growth with respect to an adapted path metric. Our approach also gives a weak form of Folz's theorem on the conservativeness as a consequence.

Original language	English
Pages (from-to)	317-347
Number of pages	31
Journal	Stochastic Processes and their Applications
Volume	124
Issue number	1
DOIs	https://doi.org/10.1016/j.spa.2013.08.004
Publication status	Published - 2014

Keywords

Escape rate
Markov chains
Upper rate function
Weighted graphs

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/j.spa.2013.08.004

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abstract = "We obtain an upper escape rate function for a continuous time minimal symmetric Markov chain defined on a locally finite weighted graph. This upper rate function, which has the same form as the manifold setting, is given in terms of the volume growth with respect to an adapted path metric. Our approach also gives a weak form of Folz's theorem on the conservativeness as a consequence.",

keywords = "Escape rate, Markov chains, Upper rate function, Weighted graphs",

author = "Xueping Huang and Yuichi Shiozawa",

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AU - Shiozawa, Yuichi

N1 - Funding Information: The research was supported partially by Project CRC701 and DFG , and by the Grant-in-Aid for Young Scientists (B) No. 23740078 .

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Y1 - 2014

N2 - We obtain an upper escape rate function for a continuous time minimal symmetric Markov chain defined on a locally finite weighted graph. This upper rate function, which has the same form as the manifold setting, is given in terms of the volume growth with respect to an adapted path metric. Our approach also gives a weak form of Folz's theorem on the conservativeness as a consequence.

AB - We obtain an upper escape rate function for a continuous time minimal symmetric Markov chain defined on a locally finite weighted graph. This upper rate function, which has the same form as the manifold setting, is given in terms of the volume growth with respect to an adapted path metric. Our approach also gives a weak form of Folz's theorem on the conservativeness as a consequence.

KW - Escape rate

KW - Markov chains

KW - Upper rate function

KW - Weighted graphs

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JF - Stochastic Processes and their Applications

IS - 1

ER -

Upper escape rate of Markov chains on weighted graphs

Abstract

Keywords

ASJC Scopus subject areas

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