2010 Fiscal Year Final Research Report
Research on Fractional Brownian Motions by the Quantum Probabilistic Method.
| Project/Area Number |
20740053
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Aichi University of Education |
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Principal Investigator |
ASAI Nobuhiro Aichi University of Education, 教育学部, 准教授 (60399029)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 量子確率論 / 直交多項式 / シーガル・バーグマン変換 / 変形フォック空間 |
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| Research Abstract |
Motivated by the classical Segal-Bargmann transform in Gaussian analysis, which has been recognized as a useful way for the analysis on the Boson Fock space, we have tried to examine the classical-quantum correspondence of random variables (stochastic processes) by constructing one-mode Fock spaces and Hilbert spaces of square integrable analytic functions with respect to non-Gaussian Bargmann measures. It is essentially related to the complex moment problem for the construction of non-Gaussian Bargmann measures. Due to this reason, it would be quite difficult to develop the general way to solve our problem in a fully general form. Therefore, in this research program our consideration has been restricted to several special cases containing the Wilson's family of orthogonal polynomials under the special choice of parameters, which is in the higher hierarchy than the Meixner's family. As a result, we have succeeded to construct several non-Gaussian Bargmann measures, explicitly.
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