Multiple Wiener integrals and nonlinear functionals of a nuclear space valued Wiener process
In this work we develop techniques for the study of nonlinear functionals of a \(\Phi'\)-valued Wiener process \(W_ t\), where \(\Phi'\) is the dual of a countably Hilbert nuclear space. We construct stochastic integrals and multiple Wiener integrals of operator-valued processes with respect to \(W_ t\). The Wiener decomposition of the space of \(\Phi'\)-valued nonlinear functionals of \(W_ t\) is established. We also obtain multiple stochastic integral expansions and representations of \(\Phi'\)-valued nonlinear functionals of \(W_ t\) as operator-valued stochastic integrals of Itô type.
operator-valued stochastic integrals of Itô type
scientific article; zbMATH DE number 4020121
scientific article