Upper estimate of martingale dimension for self-similar fractals

作者：Hino Masanori^*

来源：Probability Theory and Related Fields, 2013, 156(3-4): 739-793.

DOI：10.1007/s00440-012-0442-3

• Martingale dimension
• Self-similar set
• Sierpinski carpet
• Dirichlet form

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.

• 出版日期2013-8