Strong approximations of three-dimensional Wiener sausages

E. Csáki, Y. Hu

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We prove that the centered three-dimensional Wiener sausage can be strongly approximated by a one-dimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms of process for the normalized Wiener sausage. The proof relies on Le Gall [10]'s fine L 2-norm estimates between the Wiener sausage and the Brownian intersection local times.

Original languageEnglish
Pages (from-to)205-226
Number of pages22
JournalActa Mathematica Hungarica
Volume114
Issue number3
DOIs
Publication statusPublished - Mar 1 2007

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Keywords

  • Intersection local times
  • Strong approximation
  • Wiener sausage

ASJC Scopus subject areas

  • Mathematics(all)

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