On admissible shifts of generalized white noises

Hui-Hsiung Kuo and W. Smolenski

Journal of Multivariate Analysis, 1982, vol. 12, issue 1, 80-88

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)

Keywords: Gaussian; white; noise; Poisson; white; noise; dicohotomy; property; Radon-Nikodym; derivative; linear; kernel; space (search for similar items in EconPapers)
Date: 1982
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