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{1022855414,
author = {Hambly, B. M. and Lyons, T. J.},
title = {Stochastic area for Brownian motion on the Sierpinski
gasket},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 132-148},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855414}
}
Hambly, B. M.; Lyons, T. J. Stochastic area for Brownian motion on the Sierpinski
gasket. Ann. Probab., Tome 26 (1998) no. 1, pp. 132-148. http://gdmltest.u-ga.fr/item/1022855414/