Strassen-type functional laws for strong topologies
type: Item
instance of: scholarly article
title: Strassen-type functional laws for strong topologies
zbMATH Open document ID: 0793.60037
DOI: 10.1007/BF01199317
author: P. Deheuvels
author: M. A. Lifshits
publication date: 1994-08-11T00:00:00Z
review text: Let \(W(\cdot)\) denote a Wiener process. The functional law of the iterated logarithm due to \textit{V. Strassen} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 3, 211-226 (1964; Zbl 0132.129)] establishes that the sequence \(\{(2nLLn)^{-1/2}W(ns)\}\) of functions of \(s\in[0,1]\) is almost surely compact in the uniform topology, and gives a simple description of the corresponding limit set. We obtain a general characterization of the topologies under which this statement remains valid.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 568984
zbMATH Keywords: functional laws
zbMATH Keywords: Wiener process
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: uniform topology
zbMATH Keywords: characterization of the topologies
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 568984