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

MEDINA, JUAN MIGUEL; CERNUSCHI-FRIAS, BRUNO; RUBEN DOBARRO, FERNANDO

IEEE TRANSACTIONS ON INFORMATION THEORY

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

Año: 2020 vol. 66 p. 5866 - 5874

0018-9448

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