2013 Fiscal Year Final Research Report
Stochastic Analytical Study for Mathematical Physics of Statistical Physics and Quantum Theory
| Project/Area Number |
22740086
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Shinshu University |
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Principal Investigator |
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| Project Period (FY) |
2010-10-20 – 2014-03-31
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| Keywords | 確率偏微分方程式 / 確率解析 |
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| Research Abstract |
The aim of the present project was to consider temporal and statial regularities for stochastic partial differential equations of parabolic type driven by stable white noise, and to consider an inverse problem for stochastic linear transport equations. For the first problem, we made an approach by using a theory of complex interpolation spaces, and we discussed the convergence in a specific Banach space which has restricted integrability only. We succeeded in showing the convergence for non-symmetric independent random variables in the space which appears in constructing the solution. For the latter one, we got a nice formula to recover the deterministic coefficients from a random observation using the non-randomness of the quadratic variation process driven by a Gaussian white noise. Also we got several formulae for the problem both additive and multiplicative noise and both the noise was temporal and spatial.
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