Pathwise Kallianpur-Robbins laws for Brownian motion in the plane

• 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.

Author: Peter Mörters urn:nbn:de:hbz:386-kluedo-8048 Preprints (rote Reihe) des Fachbereich Mathematik (319) Preprint English 1998 1998 Technische Universität Kaiserslautern Kallianpur-Robbins law ; higher order; log averaging methods ; occupation measure ; planar Brownian motion ; ratio ergodic theorem ; strong theorems 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. Fachbereich Mathematik 510 Mathematik 60F15 Strong theorems 60G57 Random measures 60J55 Local time and additive functionals 60J65 Brownian motion [See also 58J65]

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