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Functional iterations and stopping times for Brownian motion on the Sierpiński gasket

Part of: Stochastic processes

Published online by Cambridge University Press:  26 February 2010

Peter J. Grabner
Peter J. Grabner
Affiliation:
Institut für Mathematik A, Technische Universitiit Graz, Steyrergasse 30, 8010 Graz, Austria, E-mail address: grabner@weyl.math.tu-graz.ac.at
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We investigate the distribution of the hitting time T defined by the first visit of the Brownian motion on the Sierpiński gasket at geodesic distance r from the origin. For this purpose we perform a precise analysis of the moment generating function of the random variable T. The key result is an explicit description of the analytic behaviour of the Laplace- Stieltjes transform of the distribution function of T. This yields a series expansion for the distribution function and the asymptotics for t →0.

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Article
Information
Mathematika , Volume 44 , Issue 2 , December 1997 , pp. 374 - 400
Copyright
Copyright © University College London 1997

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