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
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