Stochastic integration in Fock space (Q796178)

This paper uses elementary Hilbert-space techniques to construct an analogue of the Itô integral, the 'integral' taking values in the symmetric Fock space of a direct integral \(\bar {\mathcal H}\) of Hilbert spaces over the real line. (The case \(\bar {\mathcal H}=L^ 2[0,\infty)\) yields the classical Itô integral.) An explicit formula is obtained for the orthogonal projection onto the space of 'non-anticipating functionals', which is then used to establish the density of simple non- anticipating functionals. After defining the analogue of the Itô integral, its isometric nature is established. Finally, the range of this 'integral' is identified, this last being essentially the Kunita-Watanabe theorem for square-integrable martingales.