The Annals of Probability

Stochastic area for Brownian motion on the Sierpinski gasket

B. M. Hambly and T. J. Lyons

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We construct a Lévy stochastic area for Brownian motion on the Sierpinski gasket. The standard approach via Itô integrals fails because this diffusion has sample paths which are far rougher than those of semimartingales. We thus provide an example demonstrating the restrictions of the semimartingale framework. As a consequence of the existence of the area one has a stochastic calculus and can solve stochastic differential equations driven by Brownian motion on the Sierpinski gasket.

Article information

Ann. Probab., Volume 26, Number 1 (1998), 132-148.

First available in Project Euclid: 31 May 2002

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Zentralblatt MATH identifier

Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60J65: Brownian motion [See also 58J65] 60J25: Continuous-time Markov processes on general state spaces

Stochastic area differential equations fractals


Hambly, B. M.; Lyons, T. J. Stochastic area for Brownian motion on the Sierpinski gasket. Ann. Probab. 26 (1998), no. 1, 132--148. doi:10.1214/aop/1022855414.

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