| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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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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