Occupation times and Bessel densities

Yevgeniy Kovchegov; Nick Meredith; Eyal Nir

doi:10.1016/j.spl.2009.09.018

Occupation times and Bessel densities

Yevgeniy Kovchegov, Nick Meredith, Eyal Nir

Department of Chemistry

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

8 Scopus citations

Abstract

Consider a Markov process with countably many states. In order to find a one-state occupation time distribution, we use a combination of Fourier and Laplace transforms in the way that allows for the inversion of the Fourier transform. We derive a closed-form expression for the occupation time distribution in the case of a simple continuous-time random walk on Z and represent the one-state occupation density of a reversible process as a mixture of Bessel densities.

Original language	English
Pages (from-to)	104-110
Number of pages	7
Journal	Statistics and Probability Letters
Volume	80
Issue number	2
DOIs	https://doi.org/10.1016/j.spl.2009.09.018
State	Published - 15 Jan 2010

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2009.09.018

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title = "Occupation times and Bessel densities",

abstract = "Consider a Markov process with countably many states. In order to find a one-state occupation time distribution, we use a combination of Fourier and Laplace transforms in the way that allows for the inversion of the Fourier transform. We derive a closed-form expression for the occupation time distribution in the case of a simple continuous-time random walk on Z and represent the one-state occupation density of a reversible process as a mixture of Bessel densities.",

author = "Yevgeniy Kovchegov and Nick Meredith and Eyal Nir",

note = "Funding Information: We wish to thank R. Burton and M. Ossiander for sharing thoughts on the subject of this paper. We are grateful to the anonymous referee for suggesting that we include a discussion on limit behavior of f 0 ( t , x ) following Theorem 2.2 . The first author was supported in part by the Faculty Release Time fund at Oregon State University. The second author was supported by the URISC fund at Oregon State University. The third author was supported by the Human Frontier Science Program (HFSP). ",

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T1 - Occupation times and Bessel densities

AU - Kovchegov, Yevgeniy

AU - Meredith, Nick

AU - Nir, Eyal

N1 - Funding Information: We wish to thank R. Burton and M. Ossiander for sharing thoughts on the subject of this paper. We are grateful to the anonymous referee for suggesting that we include a discussion on limit behavior of f 0 ( t , x ) following Theorem 2.2 . The first author was supported in part by the Faculty Release Time fund at Oregon State University. The second author was supported by the URISC fund at Oregon State University. The third author was supported by the Human Frontier Science Program (HFSP).

PY - 2010/1/15

Y1 - 2010/1/15

N2 - Consider a Markov process with countably many states. In order to find a one-state occupation time distribution, we use a combination of Fourier and Laplace transforms in the way that allows for the inversion of the Fourier transform. We derive a closed-form expression for the occupation time distribution in the case of a simple continuous-time random walk on Z and represent the one-state occupation density of a reversible process as a mixture of Bessel densities.

AB - Consider a Markov process with countably many states. In order to find a one-state occupation time distribution, we use a combination of Fourier and Laplace transforms in the way that allows for the inversion of the Fourier transform. We derive a closed-form expression for the occupation time distribution in the case of a simple continuous-time random walk on Z and represent the one-state occupation density of a reversible process as a mixture of Bessel densities.

UR - http://www.scopus.com/inward/record.url?scp=70449651695&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2009.09.018

DO - 10.1016/j.spl.2009.09.018

M3 - Article

AN - SCOPUS:70449651695

SN - 0167-7152

VL - 80

SP - 104

EP - 110

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

Occupation times and Bessel densities

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