Distributions, Sobolev Spaces on Gaussian Vector Spaces and Ito’s Calculus

Autor: Paul Krée
Rok vydání: 1990
Předmět:
Zdroj: Stochastic Processes and their Applications ISBN: 9789401074520
DOI: 10.1007/978-94-009-2117-7_13
Popis: Two apparently very different approachs of Ito’s Calculus have been recently introduced : one is the Hida’s analysis of the white noise and the corresponding Hida distributions theory. The otherone refeers to the reformulation in terms of Sobolev spaces of Malliavin’s Calculus. The goal of the present paper is to show the relation between these two approachs, recalling also shortly under a semplified form some aspects of a distribution theory on Gaussian spaces developed in the years 1974–1978 : only real vector spaces are ae considered, the e and n seminorms on multiple tensor products are suppressed ; distributions and cylindrical distributions are simultanously studied. Also some comple­mentary results are given. The A. thanks P.A.Meyer in general and also for communication of his manuscript [P.A.ME + J.A.YA 86]. The paper is organized in the following way : I Nuclear and Complete Gaussian vector spaces. Examples connected with Ito’s Calculus. II Distribution theory on Gaussian vector spaces. III Differential Calculus in Sobolev Spaces and Ito’s Calculus. IV Kernels and Symbols of Operators on Gaussian Vector Spaces. V References.
Databáze: OpenAIRE