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Oscillating Brownian motion

Published online by Cambridge University Press:  14 July 2016

Julian Keilson and
Jon A. Wellner
Julian Keilson
Affiliation:
University of Rochester
Jon A. Wellner
Affiliation:
University of Rochester
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Abstract

An ‘oscillating' version of Brownian motion is defined and studied. ‘Ordinary' Brownian motion and ‘reflecting' Brownian motion are shown to arise as special cases. Transition densities, first-passage time distributions, and occupation time distributions for the process are obtained explicitly. Convergence of a simple oscillating random walk to an oscillating Brownian motion process is established by using results of Stone (1963).

Keywords

OSCILLATING BROWNIAN MOTIONDIFFUSION PROCESSTRANSITION PROBABILITIESARCSIN LAW

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978, pp. 300 - 310
Copyright
Copyright © Applied Probability Trust 1978 

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References

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