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

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  • Cabus, Patricia
  • Guillotin-Plantard, Nadine

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.

Suggested Citation

  • Cabus, Patricia & Guillotin-Plantard, Nadine, 2002. "Functional limit theorems for U-statistics indexed by a random walk," Stochastic Processes and their Applications, Elsevier, vol. 101(1), pages 143-160, September.
    • Handle: RePEc:eee:spapps:v:101:y:2002:i:1:p:143-160
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    References listed on IDEAS

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    1. Neuhaus, Georg, 1977. "Functional limit theorems for U-statistics in the degenerate case," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 424-439, September.
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