ABSTRACT
Let δa be the Dirac delta function at a and B(t) a Brownian motion. It was shown in Kuo [104] that δa (B(t)) is a generalized function in white noise distribution theory. More generally, it was shown in Kubo [88] that the composition F(〈·, f〉) is a generalized function for any F ∈ S ′ ( ℝ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203733813/e9279b26-91e9-40dd-8029-b908c0f36f6c/content/eq851.tif"/> and nonzero f ∈ L 2 ( ℝ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203733813/e9279b26-91e9-40dd-8029-b908c0f36f6c/content/eq852.tif"/> . Recently, generalized functions of this form have been characterized in Kubo and Kuo [90]. The Donsker delta function has also been studied in Lascheck et al. [118], H. Watanabe [172], and S. Watanabe [173] [174] [175].
