Limit theorems for the square integral of Brownian motion and its increments
type: Item
instance of: scholarly article
title: Limit theorems for the square integral of Brownian motion and its increments
zbMATH Open document ID: 0778.60025
DOI: 10.1016/0304-4149(92)90123-8
author: Wenbo V. Li
published in: Stochastic Processes and their Applications
publication date: 1993-01-16T00:00:00Z
review text: The strong laws of the iterated logarithm are proved for the integrals \[ \int^{b(T)}_{a(T)}W^ 2(t)dt, \qquad\int^{T-\alpha T}_ 0| W(t+\alpha T)-W(t)|^ 2dt \] as \(T\to\infty\), where \(1/2\leq\alpha<1\), \(W(t)\) is the standard Wiener process, \(a(T)\), \(b(T)\) are some non- decreasing functions tending to infinity. The limiting constants are calculated explicitly as solutions of some trigonometric equations.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 90073
zbMATH Keywords: strong laws of the iterated logarithm
zbMATH Keywords: Wiener process
reviewed by: Igor S. Borisov
MaRDI profile type: Publication
full work available at URL: 0304-4149(92)90123-8
OpenAlex ID: W1969580931
cites work: Q4078873
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description: scientific article; zbMATH DE number 90073