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- W2000402310 abstract "Abstract In this article, we find necessary conditions for the existence of Ito Integral in a Banach space with respect to compensated Poisson random measure (cPrm). Ito integrals with values on M-type 2 Banach spaces F of the above form exist for all measurable, adapted functions f square integrable w.r.t. β ⊗dt ( ), with β being Levy measure associated with cPrm, and have strong second moments. We show that, for general separable Banach spaces F, an inequality of the type resulting for M-type 2 Banach spaces with constant depending on cPrm is necessary and sufficient for the existence of Ito integral having second moment finite for all . It is shown that is the appropriate space in case F = H, is a separable Hilbert space. In addition, if the constant is independent of cPrm for all non-random functions in , then the Banach space is of type 2. The major technique used is Pettis Integral by Rosinski, Suchanecki [25] and a Banach Steinhaus Theorem." @default.
- W2000402310 created "2016-06-24" @default.
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- W2000402310 date "2009-10-26" @default.
- W2000402310 modified "2023-09-25" @default.
- W2000402310 title "Relation Between Stochastic Integrals and the Geometry of Banach Spaces" @default.
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- W2000402310 doi "https://doi.org/10.1080/07362990903259793" @default.
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