Operational and Banach space-valued random measures. Application to stationary series (Q2382301)

The authors consider vector measures in the space of compact operators \(\mathcal{K}(H,E)\), where \(H\) is a Hilbert space, \(E\) is a Banach space, and in the space \(L_E^2(\mathcal{A})\), with some special conditions. These measures are called operational random measure and Banach space-valued random measure, respectively. The authors study stochastic integrals with regard to these measures and propose the approximation of a strictly stationary series of elements in \(L_E^2(\mathcal{A})\) by the Fourier transform of a Banach space-valued random measure.