CONTINUITY OF AFFINE TRANSFORMATIONS OF WHITE-NOISE TEST FUNCTIONALS AND APPLICATIONS

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:43

Article

KUO, HH ; POTTHOFF, J ; YAN, JA

关键词: WHITE NOISE ANALYSIS;    AFFINE TRANSFORMATION;    WIENER SEMIGROUP;    FRECHET DERIVATIVE;    HIDA DISTRIBUTION;    TEST FUNCTIONAL;   

DOI  :  10.1016/0304-4149(92)90077-4

来源: Elsevier

【 摘 要 】

Translations and scalings defined on the Schwartz space of tempered distributions induce continuous transformations on the space of white noise test functionals [25]. Continuity of the induced transformations with respect to their parameters is proved. As a consequence one obtains a direct simple proof of the fact that the space of white noise test functionals is infinitely differentiable in Frechet sense, Moreover, it is shown that the Wiener semigroup acts as a mollifier on the space of test functionals.

【 授权许可】

Free