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Pré-Publication, Document De Travail Année : 2020

Fractional Gaussian fields on the Sierpinski gasket and related fractals

Résumé

We define and study a fractional Gaussian field $X$ with Hurst parameter $H$ on the Sierpi\'nski gasket $K$ equipped with its Hausdorff measure $\mu$. It appears as a solution, in a weak sense, of the equation $(-\Delta)^s X =W$ where $W$ is a Gaussian white noise on $L_0^2(K,\mu)$, $\Delta$ the Laplacian on $K$ and $s= \frac{d_h+2H}{2d_w}$, where $d_h$ is the Hausdorff dimension of $K$ and $d_w$ its walk dimension. The construction of those fields is then extended to other fractals including the Sierpi\'nski carpet.
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Dates et versions

hal-02505713 , version 1 (11-03-2020)

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Fabrice Baudoin, Céline Lacaux. Fractional Gaussian fields on the Sierpinski gasket and related fractals. 2020. ⟨hal-02505713⟩
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