Dirichlet forms on fractals: Poincaré constant and resistance. (English) Zbl 0767.60076

Kusuoka, Shigeo; Zhou, Xian Yin

Probab. Theory Relat. Fields 93, No. 2, 169-196 (1992).

Summary: We study Dirichlet forms associated with random walks on fractal-like finite graphs. We consider related Poincaré constants and resistance, and study their asymptotic behaviour. We construct a Markov semi-group on fractals as a subsequence of random walks, and study its properties. Finally we construct self-similar diffusion processes on fractals which have a certain recurrence property and plenty of symmetries.

MSC:

60J60	Diffusion processes
60G18	Self-similar stochastic processes

Keywords:

Dirichlet forms; Markov semi-group on fractals; self-similar diffusion processes on fractals; recurrence property

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