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

For appropriate orthonormal wavelet basis {ψ
_j
k
^e
}j
_{∈Z
k∈Zd
e∈{0,1}}
d, constants p and γ, if I
_γ
denotes the Riesz fractional integral operator of order γ and (η
_j
k
e
)
_{j∈Zk∈Zd
e∈{0,1}}
d a sequence of independent identically distributed symmetric p-stable random variables, we investigate the convergence of the series Σ
_j
k
e
η
_j
k
e
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.