TY - INPR
A1 - MÃ¶rters, Peter
T1 - The average density of planar Brownian motion
N2 - We show that the occupation measure on the path of a planar Brownian motion run for an arbitrary finite time intervalhas an average density of order three with respect to thegauge function t^2 log(1/t). This is a surprising resultas it seems to be the first instance where gauge functions other than t^s and average densities of order higher than two appear naturally. We also show that the average densityof order two fails to exist and prove that the density distributions, or lacunarity distributions, of order threeof the occupation measure of a planar Brownian motion are gamma distributions with parameter 2.
T3 - Preprints (rote Reihe) des Fachbereich Mathematik - 296
KW - Brownian motion
KW - occupation measure
KW - average density
KW - order-three density
KW - logarithmic averages
KW - density distribution
KW - lacunarity distribution
Y1 - 1997
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/822
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-7912
ER -