ScholarLens Back to search
1993•The Annals of ProbabilityOpen access

An Inversion of Strassen's Law of the Iterated Logarithm for Small Time

Nina Gantert

Open full text 18 citations

Abstract

We prove a local version of Strassen's law of the iterated logarithm. Instead of shrinking larger and larger pieces of a Brownian path and letting time go to infinity, we look at a sequence of functions we get by blowing up smaller and smaller pieces and we investigate the asymptotic behaviour of this sequence as time goes to zero. It turns out that this sequence of functions is a relatively compact subset of $C\lbrack 0, 1\rbrack$ with probability 1, and the set of its limit points is the same as in Strassen's theorem.

Open-access reader

About this research paper

What this paper is about

We prove a local version of Strassen's law of the iterated logarithm. Instead of shrinking larger and larger pieces of a Brownian path and letting time go to infinity, we look at a sequence of functions we get by blowing up smaller and smaller pieces and we investigate the asymptotic behaviour of this sequence as time goes to zero. It turns out that this sequence of functions is a relatively compact subset of $C\lbrack 0, 1\rbrack$ with probability 1, and the set of its limit points is the same as in Strassen's theorem.

Why it matters

OpenAlex reports 18 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We prove a local version of Strassen's law of the iterated logarithm. Instead of shrinking larger and larger pieces of a Brownian path and letting time go to infinity, we look at a sequence of functions we get by blowing up smaller and smaller pieces and we investigate the asymptotic behaviour of this sequence as time goes to zero. It turns out that this sequence of functions is a relatively compact subset of $C\lbrack 0, 1\rbrack$ with probability 1, and the set of its limit points is the same as in Strassen's theorem.

Key concepts: Strassen algorithm, Law of the iterated logarithm, Iterated logarithm, Mathematics, Sequence (biology), Logarithm, Central limit theorem, Mathematical analysis

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
An Inversion of Strassen's Law of the Iterated Logarithm for Small Time — Research Paper | ScholarLens