Journal of the Mathematical Society of Japan

Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets

Ben M. HAMBLY, Takashi KUMAGAI, Shigeo KUSUOKA, and Xian Yin ZHOU

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Abstract

We consider homogeneous random Sierpinski carpets, a class of infinitely ramified random fractals which have spatial symmetry but which do not have exact self-similarity. For a fixed environment we construct "natural" diffusion processes on the fractal and obtain upper and lower estimates of the transition density for the process that are up to constants best possible. By considering the random case, when the environment is stationary and ergodic, we deduce estimates of Aronson type.

Article information

Source
J. Math. Soc. Japan, Volume 52, Number 2 (2000), 373-408.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107378

Digital Object Identifier
doi:10.2969/jmsj/05220373

Mathematical Reviews number (MathSciNet)
MR1742797

Zentralblatt MATH identifier
0962.60078

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60B05: Probability measures on topological spaces 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Keywords
Sierpinski carpet random fractaj diffusion process heat equation transition densities

Citation

M. HAMBLY, Ben; KUMAGAI, Takashi; KUSUOKA, Shigeo; Yin ZHOU, Xian. Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets. J. Math. Soc. Japan 52 (2000), no. 2, 373--408. doi:10.2969/jmsj/05220373. https://projecteuclid.org/euclid.jmsj/1213107378


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