Fractional diffusion and fractional heat equation (Q2713159)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fractional diffusion and fractional heat equation |
scientific article |
Statements
Fractional diffusion and fractional heat equation (English)
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29 May 2002
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fractional Brownian motion
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Hausdorff dimension
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random field
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The authors introduce the ``fractional diffusion'' as the solution of NEWLINE\[NEWLINE{\partial\over\partial t} c(t,x)+ (I-\Delta)^{\alpha/2}(-\Delta)^{r/2} c(t,x)= \varepsilon(t,x),NEWLINE\]NEWLINE where \(\varepsilon(t,x)\) is space-time white noise and \(\Delta\) in the Laplacian. The paper is devoted to the study of the sample path properties of \(C\).
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