2016 Fiscal Year Final Research Report
Stochastic analysis for singular Wiener functional
| Project/Area Number |
26800061
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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 | University of the Ryukyus |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
|
| Keywords | 確率解析 / マリアバン解析 / 確率微分方程式 |
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| Outline of Final Research Achievements |
Stochastic differential equations with singular coefficients often appear as solutions to stochastic control problem. It is difficult to investigate such a stochastic differential equation because of its singularity. Analysis for Stochastic differential equations with boundary conditions have also similar problems.
In this research, we have tried to establish a method to investigate such stochastic
differential equations with singularity. We have obtained two main results: first we have given sufficient conditions where the distribution of the solution to stochastic differential equation with singular drift admit a transition density. We also see the Holder continuity of the transition density in space variable. Second, by using parametrix methods, we have obtained a representation formula for the distribution of the coupled solution to stochastic differential equations with reflecting boundary condition.
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| Free Research Field |
確率論
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