Ngobi, Said A generalization of the Itô formula. (English) Zbl 1011.60030 Int. J. Math. Math. Sci. 31, No. 8, 477-496 (2002). Let \(f\in L^\infty([a,b])\), \(\theta\in C^2({\mathbb R}^2)\) and \(X(t)=\int_a^tf(s)dB(s)\) be the Wiener integral. The white noise calculus is used to derive an (anticipating) version of the Itôformula for \(\theta(X(t),F)\), where \(F\in{\mathcal W}^{1/2}\), and \({\mathcal W}^{1/2}\) is a Sobolev space in the Hilbert space \((L^2)=L^2({\mathcal S}'({\mathbb R}),\mu)\), the measure \(\mu\) being the standard Gaussian measure on the space of tempered distributions \({\mathcal S}'({\mathbb R})\). This is a generalization of a well known formula, where \(F=B(c)\) for some \(c\in [a,b]\) [see H. H. Kuo, “White noise distribution theory” (1996; Zbl 0853.60001)]. Reviewer: Tomasz Bojdecki (Warszawa) MSC: 60H05 Stochastic integrals 60H40 White noise theory Keywords:white noise calculus; Hitsuda-Skorokhod integral; Itôformula Citations:Zbl 0853.60001 PDFBibTeX XMLCite \textit{S. Ngobi}, Int. J. Math. Math. Sci. 31, No. 8, 477--496 (2002; Zbl 1011.60030) Full Text: DOI EuDML