Characterizations of the white noise test functionals and hida distributions

In this paper, a characterization of the white noise test functional and Hida distributions in terms of the coefficients of their Hermite transforms is obtained. Moreover, we present a class of examples of positive generalized functional which are generally not absolutely continuous with respect to the white noise measure.

[1]  Mark S. C. Reed,et al.  Method of Modern Mathematical Physics , 1972 .

[2]  B. Øksendal,et al.  WICK MULTIPLICATION AND ITO-SKOROHOD STOCHASTIC DIFFERENTIAL EQUATIONS , 1991 .

[3]  M. Röckner,et al.  Uniqueness of generalized Schrödinger operators and applications , 1992 .

[4]  L. Streit,et al.  A Characterization of Hida Distributions , 1991 .

[5]  Barry Simon,et al.  The P(φ)[2] Euclidean (quantum) field theory , 1974 .

[6]  Bernt Øksendal,et al.  STOCHASTIC DIFFERENTIAL EQUATIONS INVOLVING POSITIVE NOISE , 1990 .

[7]  J. Potthoff.  White noise methods for stochastic partial differential equations , 1992 .

[8]  Generalized functions on infinite dimensional spaces and its application to white noise calculus , 1989 .

[9]  H. Kuo,et al.  A Characterization of White Noise Test Functionals , 1991, Nagoya Mathematical Journal.

[10]  G. Kallianpur.  Stochastic differential equations and diffusion processes , 1981 .

[11]  L. Streit,et al.  The Feynman integrand as a Hida distribution , 1991 .

[12]  Yuh-Jia Lee.  Analytic version of test functionals, Fourier transform, and a characterization of measures in white noise calculus , 1991 .

[13]  P. Meyer,et al.  Les “fonctions caractéristiques” des distributions sur l’espace de Wiener , 1991 .

[14]  Brownian functionals and applications , 1983 .

[15]  Izumi Kubo,et al.  Calculus on Gaussian white noise, II , 1980 .

[16]  H. Kuo,et al.  WHITE NOISE ANALYSIS: MATHEMATICS and APPLICATIONS , 1990 .

[17]  L. Streit,et al.  A Generalization of the characterization theorem for generalized functionals of white noise , 1991 .