A self normalized law of the iterated logarithm for random walk in random scenery |
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Authors: | Thomas M. Lewis |
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Affiliation: | (1) Department of Mathematics, Furman University, 29613 Greenville, South Carolina |
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Abstract: | LetX,Xi,i1, be a sequence of i.i.d. random vectors in d. LetSo=0 and, forn1, letSn=X1+...+Xn. LetY,Y(), d, be i.i.d. -valued random variables which are independent of theXi. LetZn=Y(So)+...+Y(Sn). We will callZn 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.Supported in part by NSF Grants DMS-85-21586 and DMS-90-24961. |
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Keywords: | Law of the Iterated Logarithm self-normalization random walk random scenery |
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