The “characteristic function” of distributions on the Wiener space. (Les “fonctions caractéristiques” des distributions sur l’espace de Wiener.) (French) Zbl 0744.60041

Meyer, P. A.; Yan, J. A.

Séminaire de probabilités, Lect. Notes Math. 1485, 61-78 (1991).

[For the entire collection see Zbl 0733.00018.]
This is an expository paper which yields some results on the characteristic functions of distributions defined on Wiener space. The main one of these results is a very simple theorem (Potthoff-Streit’s theorem) which defines completely the characteristic functions of Kubo- Yokoi’s distributions. The paper deals with Hida distribution, Fock space, Wick product, test functions, exponential test functions, trace operator, Stratonovich multiple integrals, Wiener product. Also one considers the problem of defining positive measures on Wiener spaces.

Reviewer: G.Jumarie (Montreal)

MSC:

60G20

Generalized stochastic processes

Keywords:

expository paper; characteristic functions; Wiener space; Fock space; Wick product; Stratonovich multiple integrals

Citations:

Zbl 0733.00018