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The moment problem on the Wiener space |
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| Authors: | Sergio Albeverio |
| Affiliation: | a Abteilung für Stochastik, Institut für Angewandte Mathematik der Universität Bonn, D-53115 Bonn, Germany; BiBoS (Bielefeld-Bonn-Stochastics); Sonderforschungsbereich 611 (DFG); IZKS (Bonn); CERFIM (Locarno); Accademia di Architettura (USI, Mendrisio) b Abteilung für Stochastik, Institut für Angewandte Mathematik der Universität Bonn, D-53115 Bonn, Germany; Sonderforschungsbereich 611 (DFG) |
| Abstract: | Consider an L1-continuous functional ? on the vector space of polynomials of Brownian motion at given times, suppose ? commutes with the quadratic variation in a natural sense, and consider a finite set of polynomials of Brownian motion at rational times,  , mapping the Wiener space to R.In the spirit of Schmüdgen's solution to the finite-dimensional moment problem, we give sufficient conditions under which ? can be written in the form ∫⋅dμ for some probability measure μ on the Wiener space such that μ-almost surely, all the random variables  are nonnegative. |
| Keywords: | primary, 28C20, 28E05 secondary, 44A60, 03H05, 60J65 |
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