The criterion of adaptedness of a Hilbert space valued stochastic process to the filtration generated by a cylindrical Wiener process is obtained in terms of the S-transform. The criterion is then used to establish the connection between the Ito integral with respect to a cylindrical Wiener process and the Hitsuda - Skhorohod integral in the space of Hilbert space valued stochastic distributions.
Translated title of the contributionThe Itoˆ integral and the Hitsuda-Skorohod integral in the infinite dimensional case
Original languageRussian
Pages (from-to)185-199
Number of pages15
JournalSiberian Electronic Mathematical Reports
Volume11
Publication statusPublished - 2014

    GRNTI

  • 27.43.00

    Level of Research Output

  • VAK List

ID: 6141039