Functional limit theorems for U-statistics indexed by a random walk

Patricia Cabus and Nadine Guillotin-Plantard

Stochastic Processes and their Applications, 2002, vol. 101, issue 1, 143-160

Abstract: Let (Sn)n[greater-or-equal, slanted]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 byThe walk steps will be essentially assumed centered and the space dimension d=2 or [greater-or-equal, slanted]3.

Keywords: Random; walk; Random; scenery; U-statistics; Functional; limit; theorem (search for similar items in EconPapers)
Date: 2002
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