2010 Fiscal Year Final Research Report
Stochastic least principle and its applications
| Project/Area Number |
19540157
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Hiroshima University |
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Principal Investigator |
MIKAMI Toshio Hiroshima University, 大学院・工学研究院, 教授 (70229657)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKEDA Masayoshi 東北大学, 大学院・理学研究科, 教授 (30179650)
KOIKE Shigeaki 埼玉大学, 大学院・理工学研究科, 教授 (90205295)
KAISE Hidehiro 名古屋大学, 大学院・情報科学研究科, 助教 (60377778)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 確率制御 / 最適輸送問題 / 双対定理 / KRP / KRR / log-convexity |
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| Research Abstract |
We gave maxima and maximizer of joint distribution function of maximally dependent random variables and its application. We defined a generalization of the Knothe-Rozenblatt Rearrangement (KRR)and its stochastic version Knothe-Rozenblatt process (KRP), proved the existence and the uniqueness and gave a characterization as the limit of the minimizer of a class of variational problem with a small parameter. We also gave a representation theorem for a random probability density function of a stochastic flow of KRP. We proved that the mean of a logarithm of the random probability density function with space variable replaced by KRP is convex.
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