Clark-Ocone formula by the S-transform on the Poisson white noise space | Zendy

Yuh-Jia Lee | Zendy; Nicolas Privault | Zendy; Hsin-Hung Shih | Zendy

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Clark-Ocone formula by the S-transform on the Poisson white noise space

Author(s) -

Yuh-Jia Lee,

Nicolas Privault,

Hsin-Hung Shih

Publication year - 2012

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.6.4.02

Subject(s) - white noise , white spaces , space (punctuation) , poisson distribution , noise (video) , white (mutation) , mathematics , physics , computer science , statistics , telecommunications , artificial intelligence , cognitive radio , biochemistry , chemistry , image (mathematics) , wireless , gene , operating system

Given ' a square-integrable Poisson white noise functionals we show that the Segal-Bargmann (S-) transform t 㜀! S'(Pt(g)) is absolutely continuous with d dt S '(P t(g)) = S @ E(@t'jFt ) (g) for almost all t 2 R, where Pt(g) = 1(1 , t) g for g in the Schwartz space S on R, and @t means the Poisson white noise derivative. After integration with respect to t and applying the inverse S-transform, this identity recovers the Clark-Ocone formula for '.

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