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April, 2000 Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets
Ben M. HAMBLY, Takashi KUMAGAI, Shigeo KUSUOKA, Xian Yin ZHOU
J. Math. Soc. Japan 52(2): 373-408 (April, 2000). DOI: 10.2969/jmsj/05220373


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.


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Ben M. HAMBLY. Takashi KUMAGAI. Shigeo KUSUOKA. Xian Yin ZHOU. "Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets." J. Math. Soc. Japan 52 (2) 373 - 408, April, 2000.


Published: April, 2000
First available in Project Euclid: 10 June 2008

zbMATH: 0962.60078
MathSciNet: MR1742797
Digital Object Identifier: 10.2969/jmsj/05220373

Primary: 60J60
Secondary: 60B05 , 60J35

Keywords: heat equation , random fractaj diffusion process , Sierpinski carpet , transition densities

Rights: Copyright © 2000 Mathematical Society of Japan


Vol.52 • No. 2 • April, 2000
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