Stochastic integration in Fock space

Sunder, V. S. (1986) Stochastic integration in Fock space Pacific Journal of Mathematics, 122 (2). pp. 481-491. ISSN 0030-8730

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In this paper, using purely Hubert space-theoretic methods, an analogue of the Itό integral is constructed in the symmetric Fock space of a direct integral § of Hilbert spaces over the real line. The classical Itό integral is the special case when §=L2[0, ∞). An explicit formula is obtained for the projection onto the space of 'non-anticipating functionals', which is then used to prove that simple non-anticipating functionals are dense in the space of all non-anticipating functionate. After defining the analogue of the Itό integral, its isometric nature is established. Finally, the range of this 'integral' is identified; this last result is essentially the Kunita-Watanabe theorem on square-integrable martingales.

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ID Code:53559
Deposited On:09 Aug 2011 11:47
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