3 research outputs found
Upper estimate of martingale dimension for self-similar fractals
We study upper estimates of the martingale dimension of diffusion
processes associated with strong local Dirichlet forms. By applying a general
strategy to self-similar Dirichlet forms on self-similar fractals, we prove
that for natural diffusions on post-critically finite self-similar sets
and that is dominated by the spectral dimension for the Brownian motion
on Sierpinski carpets.Comment: 49 pages, 7 figures; minor revision with adding a referenc