Occupation time distributions for the telegraph process

Leonid Bogachev; Nikita Ratanov

doi:10.1016/j.spa.2011.03.016

Occupation time distributions for the telegraph process

Leonid Bogachev
, Nikita Ratanov

Producción científica: Contribución a revista › Artículo de Investigación › revisión exhaustiva

23 Citas (Scopus)

Resumen

For the one-dimensional telegraph process, we obtain explicitly the distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process is in the range of subnormal or normal deviations from the origin; in the former case, the limit is given by the arcsine law. These limit theorems are also extended to the case of more general occupation-type functionals.

Idioma original	Inglés estadounidense
Páginas (desde-hasta)	1816-1844
Número de páginas	29
Publicación	Stochastic Processes and their Applications
Volumen	121
N.º	8
DOI	https://doi.org/10.1016/j.spa.2011.03.016
Estado	Publicada - ago. 2011

Áreas temáticas de ASJC Scopus

Estadística y probabilidad
Modelización y simulación
Matemáticas aplicadas

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10.1016/j.spa.2011.03.016

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title = "Occupation time distributions for the telegraph process",

abstract = "For the one-dimensional telegraph process, we obtain explicitly the distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process is in the range of subnormal or normal deviations from the origin; in the former case, the limit is given by the arcsine law. These limit theorems are also extended to the case of more general occupation-type functionals.",

author = "Leonid Bogachev and Nikita Ratanov",

note = "Funding Information: L. Bogachev was partially supported by a Leverhulme Research Fellowship. Both authors gratefully acknowledge partial support by the London Mathematical Society (through an LMS Scheme 2 Grant) during N. Ratanov{\textquoteright}s visit to the University of Leeds in June 2007, when part of this research was done. We are grateful to the anonymous Associate Editor for a query that encouraged us to work out a probabilistic proof of Theorem 2.4 based on the diffusion approximation ( Appendix A.3 ). Copyright: Copyright 2011 Elsevier B.V., All rights reserved.",

year = "2011",

month = aug,

doi = "10.1016/j.spa.2011.03.016",

language = "English (US)",

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AU - Bogachev, Leonid

AU - Ratanov, Nikita

N1 - Funding Information: L. Bogachev was partially supported by a Leverhulme Research Fellowship. Both authors gratefully acknowledge partial support by the London Mathematical Society (through an LMS Scheme 2 Grant) during N. Ratanov’s visit to the University of Leeds in June 2007, when part of this research was done. We are grateful to the anonymous Associate Editor for a query that encouraged us to work out a probabilistic proof of Theorem 2.4 based on the diffusion approximation ( Appendix A.3 ). Copyright: Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/8

Y1 - 2011/8

N2 - For the one-dimensional telegraph process, we obtain explicitly the distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process is in the range of subnormal or normal deviations from the origin; in the former case, the limit is given by the arcsine law. These limit theorems are also extended to the case of more general occupation-type functionals.

AB - For the one-dimensional telegraph process, we obtain explicitly the distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process is in the range of subnormal or normal deviations from the origin; in the former case, the limit is given by the arcsine law. These limit theorems are also extended to the case of more general occupation-type functionals.

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DO - 10.1016/j.spa.2011.03.016

M3 - Research Article

AN - SCOPUS:79958100700

SN - 0304-4149

VL - 121

SP - 1816

EP - 1844

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 8

ER -

Occupation time distributions for the telegraph process

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