Small scale limit theorems for the intersection local times of Brownian motion (Q1293639)

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.