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Ito stochastic integral in the dual of a nuclear space

Author

Listed:
  • Bojdecki, Tomasz
  • Jakubowski, Jacek

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.

Suggested Citation

  • Bojdecki, Tomasz & Jakubowski, Jacek, 1989. "Ito stochastic integral in the dual of a nuclear space," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 40-58, October.
    • Handle: RePEc:eee:jmvana:v:31:y:1989:i:1:p:40-58
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    Cited by:

    1. Peszat, Szymon & Zabczyk, Jerzy, 1997. "Stochastic evolution equations with a spatially homogeneous Wiener process," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 187-204, December.
    2. Bojdecki, Tomasz & Gorostiza, Luis G., 1995. "Self-intersection local time for Gaussian '(d)-processes: Existence, path continuity and examples," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 191-226, December.

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