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January 1998 Stochastic area for Brownian motion on the Sierpinski gasket
B. M. Hambly, T. J. Lyons
Ann. Probab. 26(1): 132-148 (January 1998). DOI: 10.1214/aop/1022855414

Abstract

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.

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B. M. Hambly. T. J. Lyons. "Stochastic area for Brownian motion on the Sierpinski gasket." Ann. Probab. 26 (1) 132 - 148, January 1998. https://doi.org/10.1214/aop/1022855414

Information

Published: January 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0936.60073
MathSciNet: MR1617044
Digital Object Identifier: 10.1214/aop/1022855414

Subjects:
Primary: 60J60
Secondary: 60J25, 60J65

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 1 • January 1998
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