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October 1998 The limits of Sinai's simple random walk in random environment
Yueyun Hu, Zhan Shi
Ann. Probab. 26(4): 1477-1521 (October 1998). DOI: 10.1214/aop/1022855871


We study the sample path asymptotics of a class of recurrent diffusion processes with random potentials, including examples of Sinai’s simple random walk in random environment and Brox’s diffusion process with Brownian potential. The main results consist of several integral criteria which completely characterize all the possible Lévy classes, therefore providing a very precise image of the almost sure asymptotic behaviors of these processes.


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Yueyun Hu. Zhan Shi. "The limits of Sinai's simple random walk in random environment." Ann. Probab. 26 (4) 1477 - 1521, October 1998.


Published: October 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0936.60088
MathSciNet: MR1675031
Digital Object Identifier: 10.1214/aop/1022855871

Primary: 60J15 , 60J60
Secondary: 60F15

Keywords: Integral test , Lévy's class , random environment

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 4 • October 1998
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