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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rates of convergence
of diffusions with drifted Brownian potentials


Authors: Yueyun Hu, Zhan Shi and Marc Yor
Journal: Trans. Amer. Math. Soc. 351 (1999), 3915-3934
MSC (1991): Primary 60J60, 60F05
Published electronically: May 21, 1999
MathSciNet review: 1637078
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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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Additional Information

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

Marc Yor
Affiliation: Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, 75252 Paris Cedex 05, France
Email: secret@proba.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02421-6
PII: S 0002-9947(99)02421-6
Keywords: Diffusion with random potential, Bessel process, rate of convergence
Received by editor(s): November 17, 1997
Received by editor(s) in revised form: July 3, 1998
Published electronically: May 21, 1999
Article copyright: © Copyright 1999 American Mathematical Society