The Annals of Probability

The multifractal spectrum of Brownian intersection local times

Achim Klenke and Peter Mörters

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Abstract

Let ℓ be the projected intersection local time of two independent Brownian paths in ℝd for d=2,3. We determine the lower tail of the random variable $\ell(\mathbb {U})$, where $\mathbb {U}$ is the unit ball. The answer is given in terms of intersection exponents, which are explicitly known in the case of planar Brownian motion. We use this result to obtain the multifractal spectrum, or spectrum of thin points, for the intersection local times.

Article information

Source
Ann. Probab., Volume 33, Number 4 (2005), 1255-1301.

Dates
First available in Project Euclid: 1 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1120224581

Digital Object Identifier
doi:10.1214/009117905000000116

Mathematical Reviews number (MathSciNet)
MR2150189

Zentralblatt MATH identifier
1080.60078

Subjects
Primary: 60J65: Brownian motion [See also 58J65] 60G17: Sample path properties 60J55: Local time and additive functionals

Keywords
Brownian motion intersection of Brownian paths intersection local time Wiener sausage lower tail asymptotics intersection exponent Hausdorff measure thin points Hausdorff dimension spectrum multifractal spectrum

Citation

Klenke, Achim; Mörters, Peter. The multifractal spectrum of Brownian intersection local times. Ann. Probab. 33 (2005), no. 4, 1255--1301. doi:10.1214/009117905000000116. https://projecteuclid.org/euclid.aop/1120224581


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