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arXiv · 1205.5617

Upper estimate of martingale dimension for self-similar fractals

Masanori Hino
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Abstract

We study upper estimates of the martingale dimension $d_m$ 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 $d_m=1$ for natural diffusions on post-critically finite self-similar sets and that $d_m$ is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.

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Masanori Hino. 2012-06-19. Upper estimate of martingale dimension for self-similar fractals. https://doi.org/10.1007/s00440-012-0442-3

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