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http://dx.doi.org/10.4134/BKMS.b210542

EVALUATION FORMULA FOR WIENER INTEGRAL OF POLYNOMIALS IN TERMS OF NATURAL DUAL PAIRINGS ON ABSTRACT WIENER SPACES  

Chang, Seung Jun (Department of Mathematics Dankook University)
Choi, Jae Gil (School of General Education Dankook University)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.5, 2022 , pp. 1093-1103 More about this Journal
Abstract
In this paper, we establish an evaluation formula to calculate the Wiener integral of polynomials in terms of natural dual pairings on abstract Wiener spaces (H, B, 𝜈). To do this we first derive a translation theorem for the Wiener integral of functionals associated with operators in 𝓛(B), the Banach space of bounded linear operators from B to itself. We then apply the translation theorem to establish an integration by parts formula for the Wiener integral of functionals combined with operators in 𝓛(B). We finally apply this parts formula to evaluate the Wiener integral of certain polynomials in terms of natural dual pairings.
Keywords
Abstract Wiener space; natural dual pairing; translation theorem; integration by parts formula;
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