The Annals of Applied Probability

Brownian motion in a Brownian crack

Krzysztof Burdzy and Davar Khoshnevisan

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Let D be the Wiener sausage of width $\varepsilon$ around two-sided Brownian motion. The components of two-dimensional reflected Brownian motion in D converge to one-dimensional Brownian motion and iterated Brownian motion, respectively, as $\varepsilon$ goes to 0.

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Ann. Appl. Probab., Volume 8, Number 3 (1998), 708-748.

First available in Project Euclid: 9 August 2002

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Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65] 60F99: None of the above, but in this section

Crack diffusion model iterated Brownian motion diffusion on fractal


Burdzy, Krzysztof; Khoshnevisan, Davar. Brownian motion in a Brownian crack. Ann. Appl. Probab. 8 (1998), no. 3, 708--748. doi:10.1214/aoap/1028903448.

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