A bounded law of the iterated logarithm for Hilbert space valued martingales and its application to U-statistics

Herold Dehling, Manfred Denker, Walter Philipp

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

A bounded law of the iterated logarithm for martingales with values in a separable Hilbert space H is proved. It is then applied to prove invariance principles for U-statistics for independent identically distributed (ℝ-valued) random variables {Xj, j≧1} and a kernel h: ℝm→H, m≧2, which is degenerate for the common distribution function of Xj, j≧1. This extends to general m results of an earlier paper on this subject and even gives new results in the case H=ℝ.

Original languageEnglish (US)
Pages (from-to)111-131
Number of pages21
JournalProbability Theory and Related Fields
Volume72
Issue number1
DOIs
StatePublished - Apr 1 1986

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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