The It? integral and the Hitsuda–Skorohod integral in the infinite dimensional case

摘要

The criterion of adaptedness of a Hilbert space valued stochasticprocess to the filtration generated by a cylindrical Wiener processis obtained in terms of the S-transform. The criterion is then used toestablish the connection between the It?o integral with respect to a cylindricalWiener process and the Hitsuda – Skhorohod integral in thespace of Hilbert space valued stochastic distributions.