2011 Fiscal Year Final Research Report
Asymptotic problems for viscous Hamilton-Jacobi equations with random coefficients
| Project/Area Number |
21740076
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 確率制御 / 粘性ハミルトン・ヤコビ方程式 |
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| Research Abstract |
In this research, we dealt with a class of nonlinear partial differential equations, called viscous Hamilton-Jacobi equations, which appear in stochastic optimal control problems. More specifically, we investigated the long-time behavior of solutions by both analytical and probabilistic approaches. It turned out that solutions converge to a steady state as time tends to infinity. We also succeeded in characterizing such steady state in terms of ergodic stochastic control problems
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