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Asymptotic variance parameters for the boundary local times of reflected Brownian motion on a compact interval

Part of: Special processes Stochastic analysis Markov processes

Published online by Cambridge University Press:  14 July 2016

R. J. Williams
R. J. Williams*
Affiliation:
University of California at San Diego, La Jolla
*
∗ Postal address: Department. of Mathematics, University of California, San Diego, La Jolla, CA 92093–0112, USA.
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Abstract

A direct derivation is given of a formula for the normalized asymptotic variance parameters of the boundary local times of reflected Brownian motion (with drift) on a compact interval. This formula was previously obtained by Berger and Whitt using an M/M/1/C queue approximation to the reflected Brownian motion. The bivariate Laplace transform of the hitting time of a level and the boundary local time up to that hitting time, for a one-dimensional reflected Brownian motion with drift, is obtained as part of the derivation.

Keywords

LOCAL TIMEBOUNDARY REGULATOR PROCESSLAPLACE TRANSFORMMARTINGALE

MSC classification

Primary: 60J65: Brownian motion
Secondary: 60H05: Stochastic integrals 60J55: Local time and additive functionals 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 996 - 1002
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported in part by NSF Grants DMS 8657483 and 8722351, an Alfred P. Sloan Research Fellowship, and grants from AT&T Bell Labs and SUN Microsystems.

References

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