Linear isometric non-anticipative transformations of Wiener process (Q1976602)

One gives necessary and sufficient conditions such that a non-anticipative transformation in Hilbert space defined by a Volterra kernel is isometric. The inverse isometric transformation is also defined by a Volterra kernel which is calculated. The authors use the technique of second-order stochastic processes as curves in Hilbert space. The conditions assure that the non-anticipative transformation of the Wiener process is a Wiener process too.