Strassen-type functional laws for strong topologies

Paul Deheuvels, Mikhail A. Lifshits

Research output

13 Citations (Scopus)

Abstract

Let W(·) denote a Wiener process. The functional law of the iterated logarithm due to Strassen (1964) establishes that the sequence {(2nLLn) -1/2 W(ns)} of functions of s∈[0,1] is almost surely compact in the uniform topology, and gives a simple description of the corresponding limit set. In this paper, we obtain a general characterization of the topologies under which this statement remains valid.

Original languageEnglish
Pages (from-to)151-167
Number of pages17
JournalProbability Theory and Related Fields
Volume97
Issue number1-2
DOIs
Publication statusPublished - 1 Mar 1993

Scopus subject areas

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

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