9
views
0
recommends
+1 Recommend
0 collections
0
shares
• Record: found
• Abstract: found
• Article: found
Is Open Access

# Upper estimate of martingale dimension for self-similar fractals

Preprint

Bookmark
There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

### 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.

### Most cited references16

• Record: found
• Abstract: found

### On Square Integrable Martingales

(1967)
Theory of real and time continuous martingales has been developed recently by P. Meyer [8, 9]. Let be a square integrable martingale on a probability space P. He showed that there exists an increasing process ‹X›t such that
Bookmark
• Record: found

### Function Spaces and Potential Theory

(1996)
Bookmark
• Record: found

### Dirichlet forms on fractals and products of random matrices

(1989)
Bookmark

### Author and article information

###### Journal
25 May 2012
2012-06-19
###### Article
10.1007/s00440-012-0442-3
1205.5617
7b41b84c-5fa7-4ae3-bfbd-d63b8bdac228

60G44, 28A80, 31C25, 60J60
Probab. Theory Related Fields 156 (2013), 739-793
49 pages, 7 figures; minor revision with adding a reference
math.PR