Convergence of $p$-Stable Random Fractional Wavelet Series and Some of its Properties

Juan M. Medina; Fernando R. Dobarro; Bruno Cernuschi-Frías

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arXiv · 1901.07153

Convergence of $p$-Stable Random Fractional Wavelet Series and Some of its Properties

Juan M. Medina·Fernando R. Dobarro·Bruno Cernuschi-Frías

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Abstract

For appropriate orthonormal wavelet basis $\{ψ_{j\,k}^e \}_{j\in\mathbb{Z}\,k\in\mathbb{Z}^d\,e\in\{0,1\}^d}$, constants $p$ and $γ$, if $\mathcal{I}_γ$ denotes the Riesz fractional integral operator of order $γ$ and $(η_{j\,k\,e})_{j\in\mathbb{Z} k\in\mathbb{Z}^d \,e\in\{0,1\}^d}$ a sequence of independent identically distributed symmetric $p$-stable random variables, we investigate the convergence of the series $\sum\limits_{j\,k\,e} η_{j\,k\,e} \mathcal{I}_γ ψ_{j\,k\,}^e$. Similar results are also studied for modified fractional integral operators. Finally, some geometric properties related to self similarity are studied.

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Juan M. Medina, Fernando R. Dobarro, Bruno Cernuschi-Frías. 2019-01-22. Convergence of $p$-Stable Random Fractional Wavelet Series and Some of its Properties. https://arxiv.org/abs/1901.07153

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