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 Citations (Scopus)

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

Fingerprint

U-statistics
Law of the Iterated Logarithm
Martingale
Hilbert space
Invariance Principle
Separable Hilbert Space
Identically distributed
Distribution Function
Random variable
kernel
Kernel
Distribution function
Invariance
Random variables

All Science Journal Classification (ASJC) codes

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

Cite this

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A bounded law of the iterated logarithm for Hilbert space valued martingales and its application to U-statistics. / Dehling, Herold; Denker, Manfred; Philipp, Walter.

In: Probability Theory and Related Fields, Vol. 72, No. 1, 01.04.1986, p. 111-131.

Research output: Contribution to journalArticle

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