descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1978 English Publisher:Cambridge University Press (CUP)Journal:Journal of Applied Probability, volume 15, pages 300-310 (issn: 0021-9002, eissn: 1475-6072,

Authors: Julian Keilson; Jon A. Wellner;

doi: 10.1017/s0021900200045599 , 10.2307/3213403

Oscillating Brownian motion

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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).

Related Organizations

University of Rochester
United States

Keywords

First-Passage Time Distributions, Brownian Motion, Brownian motion, Occupation Time Distributions, Diffusion processes, Distribution theory

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