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].
Citation
Masanori Hino. "Martingale dimensions for fractals." Ann. Probab. 36 (3) 971 - 991, May 2008. https://doi.org/10.1214/07-AOP349
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