Brownian motion on the Sierpinski carpet

Details Brownian motion on the Sierpinski carpet Brownian motion on the Sierpinski carpet

2008-12-09

arxiv.org/abs/0812.1802v2

Mathematics

Probability

Scientific paper

We prove that, up to scalar multiples, there exists only one local regular
Dirichlet form on a generalized Sierpinski carpet that is invariant with
respect to the local symmetries of the carpet. Consequently for each such
fractal the law of Brownian motion is uniquely determined and the Laplacian is
well defined.

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