Novel development on stochastic differential equations and Malliavin calculus
| Project/Area Number |
25800054
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Okayama University (2015-2016)
Tohoku University (2013-2014) |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 確率微分方程式 / マリアヴァン解析 / 推移確率密度関数 / 放物型偏微分方程式 / 基本解 / ヘルダー連続性 / ランダム環境 / シュタインの手法 / 確率量子場モデル / 解析半群 / ディリクレ形式 / 強フェラー性 / 経路依存型確率微分方程式 / 密度関数 / 摂動 / カップリングの手法 |
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| Outline of Final Research Achievements |
I studied the continuity in the initial value and the parameter of the density component of the transition probability density function of the solutions to stochastic differential equations with non-regular coefficients, and obtained the Hoelder continuity in the initial value under a very weak assumption on the coefficients. Moreover, I obtained the continuity which is the almost same level as that of the equation without drift term in the parameter of the density component under a weak asummption on the coefficients. The continuity of the transition probability density function is associated with the continuity in the space parameters of the fundamental solutions to second-order parabolic partial differential equations. Besides, I also obtained some results on the recurrence of the Brownian motion in random environments, and on the convergence of the distributions of random variables by Malliavin calculus and Stein's method.
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Report
(5 results)
Research Products
(25 results)
