2015 Fiscal Year Final Research Report
Studies on stochastic Fourier coefficients
| Project/Area Number |
25400135
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Aichi University of Education |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
OGAWA Shigeyoshi 立命館大学, 理工学部, 非常勤講師 (80101137)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | 確率フーリエ係数 / 非因果的関数 / Ogawa積分 / Skorokhod積分 / Malliavin解析 / 確率フーリエ変換 / Haar関数系 |
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| Outline of Final Research Achievements |
We studied the identification problem of a random function from the system of its stochastic Fourier coefficients (SFC in abbr.). We note that SFCs are determined in accordance with the choice of orthonormal basis and stochastic integrals employed to construct SFCs.
If we employ the system of trigonometric functions and Skorokhod integral to construct SFCs, then we obtained an affirmative answer to the identification problem and found a concrete procedure to reconstruct a random function from its SFCs with the aid of Brownian motion under some conditions on a random function.
If we employ the system of trigonometric functions or Haar functions and Ogawa integral to construct SFCs, then we also obtained an affirmative answer to the identification problem and found a concrete procedure to reconstruct a random function only from its SFCs without the aid of Brownian motion under some conditions on a random function.
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| Free Research Field |
確率解析
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