| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
It is known that there exit singular SPDEs. We studied high dimensional stochastic heat equations (SHE) and KPZ equations among them. For singular SPDEs, we usually define their solutions as the limit of modified SPDEs with renormalizations. In the case SHE and KPZ eq, we can find a certain regime of parameters in which the limits are solutions of the standard heat equations. We focused on the solutions' fluctuations and proved that they converged to Gaussian random variables.
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