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Discrete-time random motion in a continuous random medium

Author

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  • Boldrighini, C.
  • Minlos, R.A.
  • Pellegrinotti, A.

Abstract

We propose a discrete-time random walk on , d=1,2,..., as a variant of recent models of random walk on in a random environment which is i.i.d. in space-time. We allow space correlations of the environment and develop an analytic method to deal with them. We prove, under some general assumptions, that if the random term is small, a "quenched" (i.e., for a fixed "history" of the environment) Central Limit Theorem for the displacement of the random walk holds almost-surely. Proofs are based on L2 estimates. We consider for brevity only the case of odd dimension d, as even dimension requires somewhat different estimates.

Suggested Citation

  • Boldrighini, C. & Minlos, R.A. & Pellegrinotti, A., 2009. "Discrete-time random motion in a continuous random medium," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3285-3299, October.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:10:p:3285-3299
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    Cited by:

    1. Banerjee, Sayan & Hoffman, Christopher, 2016. "Random mass splitting and a quenched invariance principle," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 608-627.

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