Ito stochastic integral in the dual of a nuclear space

Tomasz Bojdecki and Jacek Jakubowski

Journal of Multivariate Analysis, 1989, vol. 31, issue 1, 40-58

Abstract: Ito's definition of the stochastic integral with respect to a Wiener process in the dual of a nuclear space is simplified and slightly generalized. This definition yields a completely intrinsic description of the class of random, operator-valued integrands. For a large class of spaces (e.g. for Schwartz distribution spaces) any time-inhomogeneous Wiener process is proved to have a representation as the stochastic integral with respect to a homogeneous (standard) Wiener process. A relation between this definition of stochastic integral and the notion of isometric integral in Hilbert spaces, defined by Metivier, is established.

Keywords: stochastic; integral; separable; Hilbertian; seminorm; multi-Hilbertian; space; nuclear; space; Wiener; process; in; the; dual; of; a; nuclear; space (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (2)

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