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Hitting Time Bounds for Brownian Motion on a Fractal

William B. Krebs
Proceedings of the American Mathematical Society
Vol. 118, No. 1 (May, 1993), pp. 223-232
DOI: 10.2307/2160031
Stable URL: http://www.jstor.org/stable/2160031
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Hitting Time Bounds for Brownian Motion on a Fractal
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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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