Multiple regression on stable vectors (Q1192001)

The authors study the regression \(E(Y| X_ 1,\dots,X_ n)\) for general stable vectors \((X_ 1,\dots,X_ n,Y)\) with index of stability \(0<\alpha<2\). Necessary and sufficient conditions for the linearity of the regression \(E(Y| X_ 1,\dots,X_ n)\) are established when \(1<\alpha <2\) and a sufficient condition for the finiteness of the conditional absolute moment \(E(| Y|\left| X_ 1,\dots,X_ n\right.)\) when \(0<\alpha<1\) is also given. The results obtained are applied to various classes of stable processes, such as scale mixtures of Gaussian processes, stationary moving averages and harmonizable processes.