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Generalized Poisson Functionals
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  • Published: March 1988

Generalized Poisson Functionals

  • Yoshifusa Ito1 

Probability Theory and Related Fields volume 77, pages 1–28 (1988)Cite this article

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Summary

With the aim of treating nonlinear systems with inputs being discrete and outputs being generalized functions, generalized Poisson functional are defined and analysed, where the

-transforms and the renormalizational play essential roles. For Poisson functionals, the differential operators with respect to a Poisson white noise\(\dot P\) (t), their adjoint operators and the multiplication operators by\(\dot P\) (t) are defined. Since these operators involve the time parameter explicitly, they can be used to obtain information concerning the Poisson functional at each point in time. As an example, a new method for measuring the Wiener kernels of such functionals is outlined.

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Authors and Affiliations

  1. Nagoya University College of Medical Technology, Daiko-Minami, Higashi-ku, 461, Nagoya, Japan

    Yoshifusa Ito

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  1. Yoshifusa Ito
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Ito, Y. Generalized Poisson Functionals. Probab. Th. Rel. Fields 77, 1–28 (1988). https://doi.org/10.1007/BF01848128

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  • Received: 04 May 1984

  • Revised: 24 December 1986

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF01848128

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Keywords

  • Stochastic Process
  • Nonlinear System
  • Essential Role
  • White Noise
  • Probability Theory
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