Diffusion on multifractals
(2005) Diffusion on multifractals. Nonlinear Analysis, Theory, Methods and Applications 63(5-7):pp. 2043-2056.
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Abstract
We introduce a class of random fields with variable mean-square regularity order defined on multifractal domains. The local singularity order of these random fields then depends on the initial variable mean-square regularity order, and on the variable local singularity exponent of the multifractal measure defining the local dimension of the domain considered. The theory is developed in a generalized framework through the covariance factorization, using the tools of reproducing kernel Hilbert spaces and fractional Sobolev spaces of variable order.
| Item Type: | Journal Article |
|---|---|
| Status: | Published |
| Keywords: | Generalized random fields; diffusion processes; multifractals |
| Subjects: | 230000 Mathematical Sciences > 230200 Statistics > 230202 Stochastic Analysis and Modelling |
| ID Code: | 7401 |
| Deposited By: | Anh, Vo |
| Deposited On: | 04 May 2007 |
| Alternative Locations: | http://dx.doi.org/10.1016/j.na.2005.02.107 |
| Copyright Owner: | Copyright 2005 Elsevier |
| Additional Information: | For more information, please refer to the journal’s website (see link) or contact the author. Author contact details: v.anh@qut.edu.au |