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Article Dans Une Revue ESAIM: Probability and Statistics Année : 2005

Limit theorems for U-statistics indexed by a one dimensional random walk

Résumé

Let (Sn)n≥0 be a Z-random walk and (ξx)x,Z be a sequence of independent and identically distributed R-valued random variables, independent of the random walk. Let h be a measurable, symmetric function defined on R2 with values in R. We study the weak convergence of the sequence Un,n ∈ N, with values in D[0,1] the set of right continuous real-valued functions with left limits, defined by Σ h(ξsi,ξsj)t∈ [0,1]. 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].

Dates et versions

hal-00805057 , version 1 (26-03-2013)

Identifiants

Citer

Guillotin-Plantard Nadine, Véronique Ladret. Limit theorems for U-statistics indexed by a one dimensional random walk. ESAIM: Probability and Statistics, 2005, Volume 9, p 98-115. ⟨10.1051/ps:2005004⟩. ⟨hal-00805057⟩
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