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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hitting time bounds for Brownian motion on a fractal


Author: William B. Krebs
Journal: Proc. Amer. Math. Soc. 118 (1993), 223-232
MSC: Primary 60J60
MathSciNet review: 1116263
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Abstract: We calculate a bound on hitting times for Brownian motion defined on any nested fractal. We apply this bound to show that any such process is point recurrent. We then show that any diffusion on a nested fractal must have a transition density with respect to Hausdorff measure on the underlying fractal. We also prove that any Brownian motion on a nested fractal has a jointly continuous local time with a simple modulus of space-time continuity.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1116263-X
PII: S 0002-9939(1993)1116263-X
Keywords: Diffusions, fractals
Article copyright: © Copyright 1993 American Mathematical Society