Analytic functions on abstract Wiener spaces
Let \((X,H,\mu)\) be a real abstract Wiener space. In former papers, \textit{P. Malliavan} and the author [C. R. Acad. Sci., Paris, Sér. I 322, No. 3, 261-265 (1996; Zbl 0860.60048) and J. Funct. Anal. 143, 470-528 (1997; Zbl 0873.60040)] introduced a concept of analytic functions on \(X\) and of their holomorphic prolongation. The aim of this paper is to introduce a new class of analytic functions, possessing random convergence radii. This new class turns out to be more general than the earlier one. The author proves a Cauchy formula for those functions and gives an \(L_p\)-sufficient condition for analyticity. As example, it is shown that certain stochastic line integrals as well as some solutions of stochastic differential equations are analytic Wiener functionals.
scientific article; zbMATH DE number 1579766