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

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

23 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1816-1844
Number of pages	29
Journal	Stochastic Processes and their Applications
Volume	121
Issue number	8
DOIs	https://doi.org/10.1016/j.spa.2011.03.016
State	Published - Aug 2011

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Access to Document

10.1016/j.spa.2011.03.016

Cite this

@article{60c4d537cb374ae2a658624ab568ec65,

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)",

volume = "121",

pages = "1816--1844",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier BV",

number = "8",

}

TY - JOUR

T1 - Occupation time distributions for the telegraph process

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.

UR - https://www.scopus.com/pages/publications/79958100700

UR - https://www.scopus.com/inward/citedby.url?scp=79958100700&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2011.03.016

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this