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Brownian motion with quadratic killing and some implications

Published online by Cambridge University Press:  24 August 2016

Michael L. Wenocur
Michael L. Wenocur*
Affiliation:
Ford Aerospace and Communications Corporation
*
∗Postal address: 3939 Fabian Way, Palo Alto, CA 94303, USA.
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Abstract

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

Keywords

INTEGRATED SQUARED BROWNIAN MOTIONKAC FUNCTIONALKILLING TIMESWEIBULL-LIKE RELIABILITY DISTRIBUTION
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 893 - 903
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

This paper is based in part on research supported by Army Research Office Contract DAAG29-82-K-0151 and by the Office of Naval Research Contract N00014–82-C-0620.

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