Quadratic Wiener functionals of square norms on measure spaces | Zendy

Setsuo Taniguchi | Zendy

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Quadratic Wiener functionals of square norms on measure spaces

Author(s) -

Setsuo Taniguchi

Publication year - 2008

Publication title -

communications on stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.224

H-Index - 10

eISSN - 2688-6669

pISSN - 0973-9599

DOI - 10.31390/cosa.2.1.02

Subject(s) - measure (data warehouse) , mathematics , quadratic equation , square (algebra) , pure mathematics , mathematical analysis , statistics , computer science , geometry , database

Stochastic oscillatory integrals associated with quadratic Wiener functionals obtained as square norms on measure spaces of first order Wiener chaos is investigated. As applications, the square norm of the Brownian sheet and quadratic Wiener functional related to the KdV equation will be studied. Abstract Wiener spaces were introduced by L. Gross in 1965 (3), and since then, have been playing a key role in infinite dimensional stochastic analysis. In this paper, we investigate the quadratic Wiener functional on an abstract Wiener space (X,H,") of the form F = 1 Z E (r

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