Martingale dimensions for fractals

Masanori Hino

doi:10.1214/07-AOP349

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Home > Journals > Ann. Probab. > Volume 36 > Issue 3 > Article

May 2008 Martingale dimensions for fractals

Masanori Hino

Ann. Probab. 36(3): 971-991 (May 2008). DOI: 10.1214/07-AOP349

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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].