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

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

For appropriate orthonormal wavelet basis $\{{\psi }_{jk}^e{\}}_{j\in \mathbb{Z}k\in {\mathbb{Z}}^{d}e\in \{0,1{\}}^d}$, constants $p$ and $\gamma$, if ${\mathcal{I}}_{\gamma }$ denotes the Riesz fractiona…