English

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].

Keywords

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

R2 v1 2026-06-21T09:43:13.222Z