Small scale limit theorems for the intersection local times of Brownian motion. (English) Zbl 0937.60032

Mörters, Peter; Shieh, Narn-Rueih

Electron. J. Probab. 4, Paper No. 9, 23 p. (1999).

It is proved that for local time measure on the intersection of two independent Brownian paths in \(R^3[0,1]\) the average density of order 2 a.s. exists with gauge functions \(\varphi(z)=z\). In \(R^2[0,1]\) for intersection local time of \(P\) independent Brownian paths the average density of order 2 fails to exist for any gauge function, but the average density of order 3 a.s. exists with gauge function \(z^2(\log{1\over z})^p\). Some comments and generalizations are presented.

Reviewer: N.Kalinauskaitė (Vilnius)

MSC:

60G17	Sample path properties
60J65	Brownian motion

Keywords:

intersection local time; Brownian motion