## Journal of Mathematics of Kyoto University

### Construction of diffusion processes on fractals, $d$-sets, and general metric measure spaces

#### Abstract

We give a sufficient condition to construct non-trivial $\mu$-symmetric diffusion processes on a locally compact separable metric measure space $(M,\rho , \mu )$. These processes are associated with local regular Dirichlet forms which are obtained as continuous parts of $\Gamma$-limits for approximating non-local Dirichlet forms. For various fractals, we can use existing estimates to verify our assumptions. This shows that our general method of constructing diffusions can be applied to these fractals.

#### Article information

Source
J. Math. Kyoto Univ., Volume 45, Number 2 (2005), 307-327.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281992

Digital Object Identifier
doi:10.1215/kjm/1250281992

Mathematical Reviews number (MathSciNet)
MR2161694

Zentralblatt MATH identifier
1086.60052

#### Citation

Kumagai, Takashi; Sturm, Karl-Theodor. Construction of diffusion processes on fractals, $d$-sets, and general metric measure spaces. J. Math. Kyoto Univ. 45 (2005), no. 2, 307--327. doi:10.1215/kjm/1250281992. https://projecteuclid.org/euclid.kjm/1250281992