Issue |
ESAIM: PS
Volume 9, June 2005
|
|
---|---|---|
Page(s) | 98 - 115 | |
DOI | https://doi.org/10.1051/ps:2005004 | |
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;
nadine.guillotin@univ-lyon1.fr;
veronique.ladret@univ-lyon1.fr
Received:
15
August
2004
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 [1].
Mathematics Subject Classification: 60F05 / 60J15
Key words: Random walk / random scenery / U-statistics / functional limit theorem.
© EDP Sciences, SMAI, 2005
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