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Tightness of localization and return time in random environment

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  • Hu, Yueyun

Abstract

Consider a class of diffusions with random potentials which behave asymptotically as Brownian motion. We study the tightness of localization around the bottom of some Brownian valley, and determine the limit distribution of the return time to the origin after a typical time. Via the Skorokhod embedding in random environment, we also solve the return time problem for Sinai's walk.

Suggested Citation

  • Hu, Yueyun, 2000. "Tightness of localization and return time in random environment," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 81-101, March.
    • Handle: RePEc:eee:spapps:v:86:y:2000:i:1:p:81-101
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    References listed on IDEAS

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    1. Mathieu, Pierre, 1995. "Limit theorems for diffusions with a random potential," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 103-111, November.
    2. Kesten, Harry, 1986. "The limit distribution of Sinai's random walk in random environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(1), pages 299-309.
    3. Mathieu, Pierre, 1998. "On random perturbations of dynamical systems and diffusions with a Brownian potential in dimension one," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 53-67, September.
    4. Shi, Zhan, 1998. "A local time curiosity in random environment," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 231-250, August.
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    Cited by:

    1. Andreoletti, Pierre, 2006. "On the concentration of Sinai's walk," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1377-1408, October.
    2. Diel, Roland, 2011. "Almost sure asymptotics for the local time of a diffusion in Brownian environment," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2303-2330, October.
    3. Cheliotis, Dimitris, 2008. "Localization of favorite points for diffusion in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1159-1189, July.
    4. Carlos G. Pacheco & Mariana Pérez-Rojas, 2022. "Excursions of the Brox Diffusion," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1479-1500, September.

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