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A self normalized law of the iterated logarithm for random walk in random scenery

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Abstract

LetX,X i ,i≥1, be a sequence of i.i.d. random vectors in ℤd. LetS o=0 and, forn≥1, letS n =X 1+...+X n . LetY,Y(α), α∈ℤd, be i.i.d. ℝ-valued random variables which are independent of theX i . LetZ n =Y(S o )+...+Y(S n ). We will callZ n arandom walk in random scenery.

In this work, we consider the law of the iterated logarithm for random walk in random sceneries. Under fairly general conditions, we obtain arandomly normalized law of the iterated logarithm.

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Supported in part by NSF Grants DMS-85-21586 and DMS-90-24961.

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Lewis, T.M. A self normalized law of the iterated logarithm for random walk in random scenery. J Theor Probab 5, 629–659 (1992). https://doi.org/10.1007/BF01058723

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  • DOI: https://doi.org/10.1007/BF01058723

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