Martingale dimensions for fractals

Details Martingale dimensions for fractals Martingale dimensions for fractals

2007-11-14

arxiv.org/abs/0711.2135v1

Annals of Probability, Vol. 36, No. 3 (2008), 971-991

Mathematics

Probability

22 pages, 1 figure

Scientific paper

10.1214/07-AOP349

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].

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