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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2160031
Page Count: 10
You can always find the topics here!Topics: Fractals, Brownian motion, Random walk, Vertices, Markov chains, Hausdorff measures, Markov processes, Transition probabilities, Gaskets
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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.
Proceedings of the American Mathematical Society © 1993 American Mathematical Society