White Noise Integration

Abstract

We define integrals of normal ordered monomials. These integrals are scalarly defined as sesquilinear forms over Open image in new window , the space of all symmetric, continuous functions of compact support with values in a Hilbert space \(\mathfrak{k}\). We can define products of those objects as scalarly defined integrals. We define 𝒞¹-processes and calculate their Schwartz derivatives. We prove Ito’s theorem for 𝒞¹-processes.