Rates of convergence of diffusions with drifted Brownian potentials

Hu, Yueyun; Shi, Zhan; Yor, Marc

doi:10.1090/S0002-9947-99-02421-6

Rates of convergence of diffusions with drifted Brownian potentials
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by Yueyun Hu, Zhan Shi and Marc Yor PDF

Trans. Amer. Math. Soc. 351 (1999), 3915-3934 Request permission

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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