Oscillating Brownian motion
- 1 June 1978
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 15 (2) , 300-310
- https://doi.org/10.2307/3213403
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
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