Abstract
Given a standard probability space, \( \mathbb{F}: = (\Omega ,\mathcal{F},{\{ \mathcal{F}{_{t}})_{{t \in [0,T]}}},\mathbb{P}) \) where Tââ+, consider a Wiener process W(t) taking values in Y with the covariance operator Q and a martingale \( M(t) \in \mathfrak{M}_{2}^{c}([0,T];\mathbb{H}). \).
The space \( \mathfrak{M}_{2}^{c}([0,T];\mathbb{H}). \) is defined for martingales on [0,T] in the same way that the space \( \mathfrak{M}_{2}^{c}({\mathbb{R}_{ + }};\mathbb{H}) \) for martingales on â+.
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Âİ 1990 Springer Science+Business Media Dordrecht
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Rozovskii, B.L. (1990). Linear Stochastic Evolution Systems in Hilbert Spaces. In: Stochastic Evolution Systems. Mathematics and Its Applications (Soviet Series), vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3830-7_3
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DOI: https://doi.org/10.1007/978-94-011-3830-7_3
Publisher Name: Springer, Dordrecht
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