On the distribution of the hitting time for the N–urn Ehrenfest model

Cheng Xin; Minzhi Zhao; Qiang Yao; Erjia Cui

doi:10.1016/j.spl.2019.108625

On the distribution of the hitting time for the N–urn Ehrenfest model

Cheng Xin, Minzhi Zhao, Qiang Yao, Erjia Cui

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Abstract

In this paper, we consider the N–urn Ehrenfest model. By utilizing an auxiliary continuous-time Markov chain, we obtain the explicit formula for the Laplace transform of the hitting time from a single state to a set A of states where A satisfies some symmetric properties. After obtaining the Laplace transform, we are able to compute the high-order moments (especially, variance) for the hitting time.

Original language	English (US)
Article number	108625
Journal	Statistics and Probability Letters
Volume	157
DOIs	https://doi.org/10.1016/j.spl.2019.108625
State	Published - Feb 2020
Externally published	Yes

Bibliographical note

Funding Information:
This work is partially supported by NSFC with grant numbers 11671145 and 11771286 . The second author is also partially supported by Natural Science Foundation of Zhejiang Province ( LQ18A010007 ). The third author is also partially supported by the program of China Scholarships Council (No. 201806145024 ) and the Natural Science Foundation of Shanghai ( 16ZR1409700 ).

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

Ehrenfest model
Hitting time
Laplace transform
Markov chain

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10.1016/j.spl.2019.108625

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title = "On the distribution of the hitting time for the N–urn Ehrenfest model",

abstract = "In this paper, we consider the N–urn Ehrenfest model. By utilizing an auxiliary continuous-time Markov chain, we obtain the explicit formula for the Laplace transform of the hitting time from a single state to a set A of states where A satisfies some symmetric properties. After obtaining the Laplace transform, we are able to compute the high-order moments (especially, variance) for the hitting time.",

keywords = "Ehrenfest model, Hitting time, Laplace transform, Markov chain",

author = "Cheng Xin and Minzhi Zhao and Qiang Yao and Erjia Cui",

note = "Funding Information: This work is partially supported by NSFC with grant numbers 11671145 and 11771286 . The second author is also partially supported by Natural Science Foundation of Zhejiang Province ( LQ18A010007 ). The third author is also partially supported by the program of China Scholarships Council (No. 201806145024 ) and the Natural Science Foundation of Shanghai ( 16ZR1409700 ). Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

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doi = "10.1016/j.spl.2019.108625",

language = "English (US)",

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T1 - On the distribution of the hitting time for the N–urn Ehrenfest model

AU - Xin, Cheng

AU - Zhao, Minzhi

AU - Yao, Qiang

AU - Cui, Erjia

N1 - Funding Information: This work is partially supported by NSFC with grant numbers 11671145 and 11771286 . The second author is also partially supported by Natural Science Foundation of Zhejiang Province ( LQ18A010007 ). The third author is also partially supported by the program of China Scholarships Council (No. 201806145024 ) and the Natural Science Foundation of Shanghai ( 16ZR1409700 ). Publisher Copyright: © 2019 Elsevier B.V.

PY - 2020/2

Y1 - 2020/2

N2 - In this paper, we consider the N–urn Ehrenfest model. By utilizing an auxiliary continuous-time Markov chain, we obtain the explicit formula for the Laplace transform of the hitting time from a single state to a set A of states where A satisfies some symmetric properties. After obtaining the Laplace transform, we are able to compute the high-order moments (especially, variance) for the hitting time.

AB - In this paper, we consider the N–urn Ehrenfest model. By utilizing an auxiliary continuous-time Markov chain, we obtain the explicit formula for the Laplace transform of the hitting time from a single state to a set A of states where A satisfies some symmetric properties. After obtaining the Laplace transform, we are able to compute the high-order moments (especially, variance) for the hitting time.

KW - Ehrenfest model

KW - Hitting time

KW - Laplace transform

KW - Markov chain

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VL - 157

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 108625

ER -

On the distribution of the hitting time for the N–urn Ehrenfest model

Abstract

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Keywords

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