Convergence of p-stable random fractional wavelet series and some of Its properties

Abstract

For appropriate orthonormal wavelet basis {ψ^e_jk} j∈Zk∈Z^de∈{0,1}^d, constants p and γ , if I_γ denotes the Riesz fractional integral operator of order γ and (ηjke)j∈Zk∈Z^de∈{0,1}^d a sequence of independent identically distributed symmetric p -stable random variables, we investigate the convergence of the series ∑_jkeηjkeI_γψ^ejk . Similar results are also studied for modified fractional integral operators. Finally, some geometric properties related to self similarity are studied.