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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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Metadaten
Verfasserangaben:Peter Mörters
URN (Permalink):urn:nbn:de:hbz:386-kluedo-8048
Schriftenreihe (Bandnummer):Preprints (rote Reihe) des Fachbereich Mathematik (319)
Dokumentart:Preprint
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:1998
Jahr der Veröffentlichung:1998
Veröffentlichende Institution:Technische Universität Kaiserslautern
Datum der Publikation (Server):28.01.2000
Freies Schlagwort / Tag:Kallianpur-Robbins law; higher order; log averaging methods; occupation measure; planar Brownian motion; ratio ergodic theorem; strong theorems
Bemerkung:
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.
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Klassifikation (Mathematik):60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Fxx Limit theorems [See also 28Dxx, 60B12] / 60F15 Strong theorems
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G57 Random measures
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J55 Local time and additive functionals
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J65 Brownian motion [See also 58J65]
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011