Diffusion on multifractals. (English) Zbl 1224.60111
Summary: 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.
MSC:
| 60G60 | Random fields |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 47G30 | Pseudodifferential operators |
Keywords:
anomalous diffusion; fractional diffusion; fractals; multifractals; generalized random fieldsReferences:
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