Abstract
Let M be a square integrable (real valued, right continuous) martingale relative to a certain filtration. Then the starting point of stochastic integration theory is the L2-isometry between the space of square integrable predictable functions X (relative to the Doléans measure of M2) and the space of the stochastic integrals ∫XdM. This result extends without major difficulties to the case that M is Hilbert space valued and X belongs to a suitable space of operator-valued predictable functions.
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© 1985 D. Reidel Publishing Company
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Dettweiler, E. (1985). Stochastic Integration of Banach Space Valued Functions. In: Arnold, L., Kotelenez, P. (eds) Stochastic Space—Time Models and Limit Theorems. Mathematics and Its Applications, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5390-1_4
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DOI: https://doi.org/10.1007/978-94-009-5390-1_4
Publisher Name: Springer, Dordrecht
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