2014 Fiscal Year Final Research Report
stochastic analysis for jump processes and their asymptotic expansions
| Project/Area Number |
24540175
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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 | Ehime University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
YAMANOBE Takanobu 北海道大学, 医学研究科, 助教 (00322800)
HAYASHI Tadafumi 琉球大学, 理工学研究科, 助教 (90532549)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 確率解析 / ジャンプ過程 / マリアバン解析 |
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| Outline of Final Research Achievements |
We have constructed Sobolev spaces over the Wiener-Poisson space. We have applied these Sobolev norms to the analysis of Ito type stochastic differential equations (SDEs) on the Wiener-Poisson space. We showed the existence and smoothness of the transition density function of the Wiener-Poisson functionals. Further, we gave asymptotic expansion of the functionals with respect to parameters, which appear in mathematical finance.
As for application in medicine, we have constructed a mathematical model using SDE which describes activities of the axon of squids. We also calculated the transition density function for the electric potential of the axon in this model.
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| Free Research Field |
確率解析
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