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.

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Author:Peter Mörters
URN (permanent link):urn:nbn:de:hbz:386-kluedo-8048
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (319)
Document Type:Preprint
Language of publication:English
Year of Completion:1998
Year of Publication:1998
Publishing Institute:Technische Universität Kaiserslautern
Tag: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.
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):60F15 Strong theorems
60G57 Random measures
60J55 Local time and additive functionals
60J65 Brownian motion [See also 58J65]

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