stochastic partial differential equation
Stochastic integration with respect to the cylindrical Wiener process via regularization
The author defines an integral with respect to a cylindrical Brownian motion on a separable Hilbert space \(V\) with covariance matrix given by a self-adjoint operator \(V\) following the ideas of \textit{F. Russo} and \textit{P. Vallois} [Probab. Theory Relat. Fields 97, No. 3, 403--421 (1993; Zbl 0792.60046)] on integration via regularization. The defined integral is an extension of the classical one. The author's method is based on the representation of the stochastic integral with respect to the cylindrical Wiener process as a series of standard stochastic integrals with respect to components of the cylindrical Wiener process. As an application, he proves the existence of a solution of a parabolic stochastic partial differential equation with anticipating initial data.
scientific article; zbMATH DE number 6222498
scientific article