TY - INPR
A1 - MÃ¶rters, Peter
T1 - Density theorems for the intersection local times of planar Brownian motion
N2 - We show that the intersection local times \(\mu_p\) on the intersection of \(p\) independent planar Brownian paths have an average density of order three with respect to the gauge function \(r^2\pi\cdot (log(1/r)/\pi)^p\), more precisely, almost surely, \[ \lim\limits_{\varepsilon\downarrow 0} \frac{1}{log |log\ \varepsilon|} \int_\varepsilon^{1/e} \frac{\mu_p(B(x,r))}{r^2\pi\cdot (log(1/r)/\pi)^p} \frac{dr}{r\ log (1/r)} = 2^p \mbox{ at $\mu_p$-almost every $x$.} \] We also show that the lacunarity distributions of \(\mu_p\), at \(\mu_p\)-almost every point, is given as the distribution of the product of \(p\) independent gamma(2)-distributed random variables. The main tools of the proof are a Palm distribution associated with the intersection local time and an approximation theorem of Le Gall.
T3 - Preprints (rote Reihe) des Fachbereich Mathematik - 303
KW - Brownian motion
KW - intersection local time
KW - Palm distribution
KW - average density
KW - lacunarity distribution
KW - density distribution
KW - logarithmic average
Y1 - 1999
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/829
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-7988
N1 - The paper is a continuation of Number 296 of the same series and will be embedded in a larger joint project with N.R.Shieh (Taipeh).
ER -