Construction of diffusion processes on fractals, $d$-sets, and general metric measure spaces
Kumagai, Takashi ; Sturm, Karl-Theodor
J. Math. Kyoto Univ., Tome 45 (2005) no. 4, p. 307-327 / Harvested from Project Euclid
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.
Publié le : 2005-05-15
Classification:  60J60,  28A80,  31C25,  49Q20,  60J35,  60J45
@article{1250281992,
     author = {Kumagai, Takashi and Sturm, Karl-Theodor},
     title = {Construction of diffusion processes on fractals, $d$-sets, and general metric measure spaces},
     journal = {J. Math. Kyoto Univ.},
     volume = {45},
     number = {4},
     year = {2005},
     pages = { 307-327},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250281992}
}
Kumagai, Takashi; Sturm, Karl-Theodor. Construction of diffusion processes on fractals, $d$-sets, and general metric measure spaces. J. Math. Kyoto Univ., Tome 45 (2005) no. 4, pp.  307-327. http://gdmltest.u-ga.fr/item/1250281992/