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

For appropriate orthonormal wavelet basis {psi(e)(jk)}(j is an element of Zk is an element of Zd e)is an element of({0,1}d), constants p and gamma, if I-gamma denotes the Riesz fractional integral operator of order gamma and (eta(j k e))(j is an element of Zk is an element of Zd e is an element of{0,1}d) a sequence of independent identically distributed symmetric p-stable random variables, we investigate the convergence of the series Sigma(j k e) eta I-j k e(gamma) psi(e)(j k). Similar results are also studied for modified fractional integral operators. Finally, some geometric properties related to self similarity are studied.