On theL2-Theory of product stochastic measures and multiple wiener–ito integrals

Abstract

In this work we construct product stochastic measures using symmetric tensor products in appropriate Hilbert spaces and then construct multiple Wiener-Itô integrals using the vector valued measure approach. A clear relationship between the theories of L 2 -multiple stochastic integrals and vector valued measures is established. This approach yields, as special cases, the multiple stochastic integrals of Itô Surgailis, Ogura, and Fox and Taqqu, among others