Convergence of U-statistics indexed by a random walk to stochastic integrals of a Levy sheet

Brice Franke, Françoise Pène, Martin Wendler

Type: Preprint

Publication Date: 2014-01-30

Citations: 0

Abstract

We establish limit theorems for U-statistics indexed by a random walk on Z^d and we express the limit in terms of some Levy sheet Z(s,t). Under some hypotheses, we prove that the limit process is Z(t,t) if the random walk is transient or null-recurrent ant that it is some stochastic integral with respect to Z when the walk is positive recurrent. We compare our results with results for random walks in random scenery.

Locations

arXiv (Cornell University) - View - PDF
Project Euclid (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF

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+	Distances of Probability Measures and Random Variables	2010	R. M. Dudley
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+ PDF Chat	Asymptotic Behavior of the Local Time of a Recurrent Random Walk	1984	Naresh C. Jain William E. Pruitt
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