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On admissible shifts of generalized white noises

Author

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  • Kuo, Hui-Hsiung
  • Smolenski, W.

Abstract

Let be the Schwartz space of rapidly decreasing real functions. The dual space * consists of the tempered distributions and the relation [subset of] L2() [subset of] * holds. Let [gamma] be the Gaussian white noise on * with the characteristic functional , [xi] [set membership, variant] , where [short parallel]·[short parallel] is the L2()-norm. Let [nu] be the Poisson white noise on * with the characteristic functional = exp[Upsilon][integral operator] {[exp(i[xi](t)u)] - 1 - (1 + u2)-1(i[xi](t)u)} d[eta](u)dt), [xi] [set membership, variant] , where the Lévy measure is assumed to satisfy the condition [integral operator]u2d[eta](u)

Suggested Citation

  • Kuo, Hui-Hsiung & Smolenski, W., 1982. "On admissible shifts of generalized white noises," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 80-88, March.
    • Handle: RePEc:eee:jmvana:v:12:y:1982:i:1:p:80-88
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