Volume 9, June 2005
|Page(s)||98 - 115|
|Published online||15 November 2005|
Limit theorems for U-statistics indexed by a one dimensional random walk
Université Claude Bernard,
Lyon 1, 50 av. Tony-Garnier, 69366 Lyon Cedex 07, France;
Let (Sn)n≥0 be a -random walk and be a sequence of independent and identically distributed -valued random variables, independent of the random walk. Let h be a measurable, symmetric function defined on with values in . We study the weak convergence of the sequence , with values in D[0,1] the set of right continuous real-valued functions with left limits, defined by Statistical applications are presented, in particular we prove a strong law of large numbers for U-statistics indexed by a one-dimensional random walk using a result of .
Mathematics Subject Classification: 60F05 / 60J15
Key words: Random walk / random scenery / U-statistics / functional limit theorem.
© EDP Sciences, SMAI, 2005
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