Transactions of the American Mathematical Society

Author(s): Yueyun Hu; Zhan Shi; Marc Yor
Journal: Trans. Amer. Math. Soc. 351 (1999), 3915-3934.
MSC (1991): Primary 60J60, 60F05
Posted: May 21, 1999
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Abstract: We are interested in the asymptotic behaviour of a diffusion process with drifted Brownian potential. The model is a continuous time analogue to the random walk in random environment studied in the classical paper of Kesten, Kozlov, and Spitzer. We not only recover the convergence of the diffusion process which was previously established by Kawazu and Tanaka, but also obtain all the possible convergence rates. An interesting feature of our approach is that it shows a clear relationship between drifted Brownian potentials and Bessel processes.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 60J60, 60F05

Yueyun Hu
Affiliation: Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, 75252 Paris Cedex 05, France
Email: hu@proba.jussieu.fr

Zhan Shi
Affiliation: Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, 75252 Paris Cedex 05, France
Email: shi@ccr.jussieu.fr

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