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 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Hiroshima University |
Principal Investigator |
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Project Period (FY) |
2009 – 2011
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Project Status |
Completed (Fiscal Year 2011)
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Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | 確率制御 / 粘性ハミルトン・ヤコビ方程式 / 長時間挙動 / 漸近問題 / ベルマン方程式 / 拡散過程 / エルゴード性 / リヤプノフの方法 |
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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Report
(4 results)
Research Products
(72 results)
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[Presentation] 確率論と非線形偏微分方程式2010
Author(s)
Naoyuki Ichihara
Organizer
確率論ヤングサマーセミナー2010
Place of Presentation
グランパスイン白浜(和歌山県)
Year and Date
2010-08-18
Related Report
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