Martingale dimensions for fractals

• 成果类型: Article
• 署名作者: Hino, Masanori
• 署名单位: Kyoto University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP349
• 发表日期: 2008
• 页码: 971-991
• 关键词: self-similar sets; energy measures; singularity

摘要

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].