TY - INPR
A1 - MÃ¶rters, Peter
T1 - Pathwise Kallianpur-Robbins laws for Brownian motion in the plane
N2 - The Kallianpur-Robbins law describes the long term asymptotic behaviour of the distribution of the occupation measure of a Brownian motion in the plane. In this paper we show that this behaviour can be seen at every typical Brownian path by choosing either a random time or a random scale according to the logarithmic laws of order three. We also prove a ratio ergodic theorem for small scales outside an exceptional set of vanishing logarithmic density of order three.
T3 - Preprints (rote Reihe) des Fachbereich Mathematik - 319
KW - planar Brownian motion
KW - occupation measure
KW - strong theorems
KW - Kallianpur-Robbins law
KW - ratio ergodic theorem
KW - log averaging methods
KW - higher order
Y1 - 1998
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/840
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-8048
N1 - Dies ist die lange Version der Arbeit "Almost sure Kallianpur-Robbins laws for Brownian motion in the plane", die in Prob. Theory rel. Fields erscheint.
ER -