ランダムな係数を持つ粘性ハミルトン・ヤコビ方程式の漸近問題

2011 年度 研究成果報告書

• 研究課題/領域番号: 21740076
• 研究種目: 若手研究(B)
• 配分区分: 補助金
• 研究分野: 数学一般(含確率論・統計数学)
• 研究機関: 広島大学
• 研究代表者: 市原 直幸 広島大学, 大学院・工学研究院, 准教授 (70452563)
• 研究期間 (年度): 2009 – 2011
• キーワード: 確率制御 / 粘性ハミルトン・ヤコビ方程式

研究概要

本研究では,確率最適制御問題に現れる粘性ハミルトン・ヤコビ方程式と呼ばれる非線形偏微分方程式を取り扱った.具体的には,解が長時間経過後にどのような挙動を示すのかを確率論と偏微分方程式の手法を用いて考察した.その結果,粘性ハミルトン・ヤコビ方程式の解はある定常状態に近づくことがわかった.さらに,その定常状態をエルゴード型確率最適制御問題の言葉で特徴づけることができた

研究成果

• [雑誌論文] Large time asymptotic problems for optimal stochastic control with superlinear cost (2012)
  • 著者名/発表者名: Naoyuki Ichihara
  • 雑誌名: Stochastic Processes and the irApplications 巻: 122(4) ページ: 1248-1275
  • DOI: DOI:10.1016/j.spa.2011.12.005
  • 査読あり
• [雑誌論文] Recurrence and transience of optimal feedback processes associated with Bellman equations of ergodic type (2011)
  • 著者名/発表者名: Naoyuki Ichihara
  • 雑誌名: Recurrence and transience of optimal feedback processes associated with Bellman equations of ergodic type 巻: 49(5) ページ: 1938-1960
  • DOI: DOI:10.1137/090772678
  • 査読あり
• [雑誌論文] Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians (2009)
  • 著者名/発表者名: Naoyuki Ichihara
  • 雑誌名: 京都大学数理解析研究所講究録 巻: 1651 ページ: 137-160
  • URL: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1651-12.pdf
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellman equations with superlinear nonlinearity in gradients (2012)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Probability seminar
  • 発表場所: National Central University, Taiwan
  • 年月日: 2012-03-21
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellmane quations with superlinear nonlinearity in gradients (2012)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Probability seminar
  • 発表場所: National ChiaoTung University, Taiwan
  • 年月日: 2012-03-19
• [学会発表] Large time asymptotic problems for stochastic optimal control (2012)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Mathematical physics and Stochasticanalysis
  • 発表場所: Shonan village center, Kanagawa
  • 年月日: 2012-03-14
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellmane quations with superlinear nonlinearity in gradients (2012)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: CREST and 4th Ritsumeikan-Florence Workshop on Risk, Simulation and Related Topics
  • 発表場所: Ritsumeikan Asia Pacific University, Beppu
  • 年月日: 2012-03-08
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellman equations with superlinear nonlinearity in gradients (2012)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: 13th Workshop on Nonlinear Partial Differential Equations
  • 発表場所: Waseda University, Tokyo
  • 年月日: 2012-03-05
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellman equations with superlinear nonlinearity in gradients (2012)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Seminaire d' analyse appliquee, Universite de Bretagne Occidentale
  • 発表場所: Brest, France
  • 年月日: 2012-02-21
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellman equations with superlinear nonlinearity in gradients (2012)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Analysis seminar
  • 発表場所: Kobeuniversity, Kobe
  • 年月日: 2012-02-09
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellmanequations with superlinear nonlinearity in gradients (2011)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Dynamical Optimization in PDE and Geometry
  • 発表場所: Universite Bordeaux 1, Bordeaux, France
  • 年月日: 2011-12-19
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellmanequations with superlinear nonlinearity in gradients (2011)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Osaka probability seminar
  • 発表場所: Osaka University.
  • 年月日: 2011-10-18
• [学会発表] Large timeasymptotic problems for viscousHamilton-Jacobi equations (2011)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: MSJ meeting 2011
  • 発表場所: Shinshu University
  • 年月日: 2011-09-29
• [学会発表] Large time asymptotic problems for some optimal stochastic control and associated partial differential equations (2011)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Hiroshima AppliedAnalysis seminar(16th)
  • 発表場所: Hiroshima Univeristy
  • 年月日: 2011-08-31
• [学会発表] Large time asymptotic problems for optimal stochastic control with superlinear cost (2011)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Large timeasymptotic problems for optimal stochasticcontrol with superlinear cost
  • 発表場所: Kyusyu Univeristy.
  • 年月日: 2011-07-08
• [学会発表] Large time asymptotic problems for somestochastic control (2011)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Tokyo probability seminar
  • 発表場所: Tokyo Institute of Technology
  • 年月日: 2011-06-06
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellmane quations with quadratic nonlinearity ingradients (2011)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Journee a Tours, Universite deTours
  • 発表場所: Tours, France
  • 年月日: 2011-03-02
• [学会発表] On the large timebehavior of solutions of Hamilton-Jacobi-Bellman equations (2011)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Okayama Probability and Analysisseminar
  • 発表場所: Okayama University
  • 年月日: 2011-02-18
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellmanequations with quadratic nonlinearity in gradients (2010)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Probability seminar
  • 発表場所: National ChiaoTung University, Taiwan
  • 年月日: 2010-11-25
• [学会発表] Optimal control theory and partial differential e quations (2010)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Colloquium at Department of Mathe matics
  • 発表場所: National Central University, Taiwan
  • 年月日: 2010-10-21
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellmanequations with quadratic nonlinearity in gradients (2010)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Probability seminar
  • 発表場所: Academia Sinica, Taiwan
  • 年月日: 2010-09-27
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellmanequations with quadratic nonlinearity in gradients (2010)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: SPA 2010 Osaka
  • 発表場所: Senri Life Science Center, Osaka
  • 年月日: 2010-09-06
• [学会発表] Probability the oryand nonlinear partial differentiale quations (2010)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Probability YSS 2010
  • 発表場所: Grampusinn Shirahama, Wakayama
  • 年月日: 2010-08-18
• [学会発表] Large time behavior of solutions of Hamilton-Jacobi-Bellmane quations with quadratic nonlinearity in gradients (2010)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Symposium" Viscosity methodsand nonlinear PDE"
  • 発表場所: Hokkaido University
  • 年月日: 2010-07-23
• [学会発表] On the large timebehavior of solutions of Hamilton-Jacobi-Bellman equations (2010)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: MSJmeeting 2010
  • 発表場所: Keio University
  • 年月日: 2010-03-25
• [学会発表] Viscous Hamilton-Jacobi equations and associated diffusion processes (2010)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Seminaire d' analysenumeruque, Universite de Rennes1
  • 発表場所: Rennes, France
  • 年月日: 2010-02-18
• [学会発表] Viscous Hamilton-Jacobi equations and associated diffusion processes (2010)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Seminaire d' analyseappliquee, Universite de BretagneOccidental
  • 発表場所: Brest, France
  • 年月日: 2010-02-16
• [学会発表] On the ergodic problem for viscous Hamilton-Jacobie quations (2010)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Fukae Workshop on Differential Equations
  • 発表場所: Kobe University
  • 年月日: 2010-01-22
• [学会発表] Recurrence and transience of optimal feedback processesassociated with Bellman equations of ergodic type (2009)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Probability seminar, Institute of Mathe matics
  • 発表場所: Academia Sinica. China
  • 年月日: 2009-12-02
• [学会発表] On the ergodic problem for viscous Hamilton-Jacobie quations (2009)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Stochastic Problems and Nonlinear PDEs
  • 発表場所: Kyoto University
  • 年月日: 2009-11-30
• [学会発表] Recurrence andtransience of diffusion processes associatedwith Bellman equations of ergodic type (2009)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: One day seminar" Finance, Stochastics andAsymptotic analysis"
  • 発表場所: Osaka University
  • 年月日: 2009-11-28
• [学会発表] Recurrence andtransience of diffusion processes associatedwith nonlinear differential equations (2009)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Probability seminar
  • 発表場所: National ChiaoTung University, Taiwan
  • 年月日: 2009-11-11
• [学会発表] On the recurrence of diffusion processes associated with viscous Hamilton-Jacobi equations (2009)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: viscous Hamilton-Jacobi equations, Kansaiprobability seminar
  • 発表場所: Kyoto University
  • 年月日: 2009-10-16
• [学会発表] On the recurrence of diffusion processes associated with viscous Hamilton-Jacobi equations (2009)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: Markovprocesses and stochastic analysis
  • 発表場所: Okayama University
  • 年月日: 2009-10-10
• [学会発表] On the ergodic problem for viscous Hamilton-Jacobiequations (2009)
  • 著者名/発表者名: Naoyki Ichihara
  • 学会等名: MSJ meeting 2009
  • 発表場所: Osaka University
  • 年月日: 2009-09-25
• [備考]
  • URL: http://home.hiroshima-u.ac.jp/~naoyuki/index.html