On the span of Brownian motion in a field in one dimension

Yu.A. Makhnovskii, M.E. Maslova and A.M. Berezhkovskii

Physica A: Statistical Mechanics and its Applications, 1996, vol. 225, issue 2, 221-234

Abstract: We study the effect of a field on the span of a particle diffusing on a line, i.e., the length covered by a Brownian particle which moves on a line for time t in the presence of a constant field. This is the one-dimensional analog of the Wiener sausage volume. Exact expressions are found for the probability density for the span together with the first two moments. Our results indicate that at very short times the dominant effect is diffusion while at very long times the field plays the dominant role.

Keywords: Brownian motion; Wiener sausage; Diffusion; Drift (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:225:y:1996:i:2:p:221-234

DOI: 10.1016/0378-4371(95)00417-3

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