On stochastic integration by series of Wiener integrals
\textit{D. E. Varberg} [Ann. Math. Stat. 37, 567-576 (1966; Zbl 0143.206)] defined a certain stochastic integral as the limit of suitable orthogonal series of random variables which are closely related to the martingale differences, and noted that the resulting integral is more general than the Wiener integral in some respects. The present paper abstracts that construction and obtains the corresponding results in a somewhat more general context. Thus one has: ``Stochastic integrals of random functions with respect to a white noise random measure are defined in terms of random series of the usual Wiener integrals. Conditions for the existence of such integrals are obtained in terms of the nuclearity of certain operators on \(L^ 2\)- spaces. The relation with the Fisk-Stratonovich symmetric integral is also discussed.'' The paper contains several examples to illustrate the significance of the thus obtained generalization. In particular neither integral includes the other although they have a ``large'' intersection.
scientific article; zbMATH DE number 4080539