Thin Points of Brownian Motion Intersection Local Times

Achim Klenke ()
Additional contact information
Achim Klenke: Johannes-Gutenberg Universität Mainz, Fachbereich Mathematik und Informatik

A chapter in Interacting Stochastic Systems, 2005, pp 295-303 from Springer

Abstract: Summary Let $$\ell $$ be the projected intersection local time of two independent Brownian paths in $$\mathbb{R}^d $$ for d = 2, 3. We determine the lower tail of the random variable $$\ell $$ (B(0, 1)), where B(0, 1) 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.

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 (search for similar items in EconPapers)
Date: 2005
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-27110-9_13

Ordering information: This item can be ordered from
http://www.springer.com/9783540271109

DOI: 10.1007/3-540-27110-4_13

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().