Martingale dimensions for fractals
Probability
2008-04-22 v1
Abstract
We prove that the martingale dimensions for canonical diffusion processes on a class of self-similar sets including nested fractals are always one. This provides an affirmative answer to the conjecture of S. Kusuoka [Publ. Res. Inst. Math. Sci. 25 (1989) 659--680].
Cite
@article{arxiv.0711.2135,
title = {Martingale dimensions for fractals},
author = {Masanori Hino},
journal= {arXiv preprint arXiv:0711.2135},
year = {2008}
}
Comments
22 pages, 1 figure