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Functional iterations and stopping times for Brownian motion on the Sierpiński gasket
Author(s) -
Grabner Peter J.
Publication year - 1997
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300012699
Subject(s) - mathematics , brownian motion , laplace transform , geodesic , mathematical analysis , distribution (mathematics) , sierpinski triangle , function (biology) , moment (physics) , brownian excursion , diffusion process , fractal , geometric brownian motion , statistics , classical mechanics , knowledge management , innovation diffusion , evolutionary biology , computer science , biology , physics
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.