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August, 1993 A Limit Theorem for Functionals of Jumps of Birth and Death Processes under Heavy Traffic Condition
Keigo Yamada, Sung Jo Hong
Ann. Appl. Probab. 3(3): 840-862 (August, 1993). DOI: 10.1214/aoap/1177005367

Abstract

For a class of birth and death processes under a heavy traffic condition, the asymptotic behavior of functionals of their jumps is investigated. It is shown that, under suitable normalization, the functionals converge in law to a process that is the sum of a Brownian motion and a constant times the local time of a reflecting Brownian motion at zero. Some applications to queueing processes are presented.

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Keigo Yamada. Sung Jo Hong. "A Limit Theorem for Functionals of Jumps of Birth and Death Processes under Heavy Traffic Condition." Ann. Appl. Probab. 3 (3) 840 - 862, August, 1993. https://doi.org/10.1214/aoap/1177005367

Information

Published: August, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0780.60035
MathSciNet: MR1233629
Digital Object Identifier: 10.1214/aoap/1177005367

Subjects:
Primary: 60F17
Secondary: 60H30 , 60K25

Keywords: birth and death processes , functionals of jumps , heavy traffic condition , limit theorem , Local time , Reflecting Brownian motion

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.3 • No. 3 • August, 1993
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