2000 年度実績報告書

確率論の総合的研究

研究課題

研究課題/領域番号	11304003
研究機関	東京大学
研究代表者	舟木直久東京大学, 大学院・数理科学研究科, 教授 (60112174)
研究分担者	重川一郎京都大学, 理学研究科, 教授 (00127234) 内山耕平東京工業大学, 理工学研究科, 教授 (00117566) 竹田雅好東北大学, 理学研究科, 教授 (30179650) 樋口保成神戸大学, 理学部, 教授 (60112075) 長井英生大阪大学, 基礎工学研究科, 教授 (70110848)
キーワード	確率解析 / マルコフ過程 / 流体力学極限 / ランダム行列 / 確率制御 / エルゴード理論 / 無限粒子系 / ディリクレ形式
研究概要	今年度は下記のように研究集会を9回開催した。 1.確率論サマースクール 2.無限粒子系とパーコレーション 3.ランダム行列とその周辺 4.Infinite Dimensional Stochastic Analysis and Related Fields 5.流体力学極限 6.Stochastic Control and Related Topics 7.Ergodic Theory and Related Topics 8.確率論とPDE 9.確率過程とその周辺 1では竹田雅好氏による連続講演「Dirichlet形式入門」が行われた。また、この分野の第一人者である福島正俊氏の講演もあり、若手研究者には多いに刺激になった。2ではMinimal Spanning TreeやConformal Invarianceに関する最新の話題を紹介する講義があった。3では、ランダム行列のスペクトルおよびそれに関連する話題についての報告があった。4では、本科研費の援助によりS.Albeverio,R.Leandreの両氏を招聘した。同時にA.Sengupta,A.Hahnの両氏の参加も得た。Albeverio氏は、場の量子論と無限次元確率解析の関係について講演し、Leandre氏はウィッテンの剛性定理に関する講演を行った。5では、T.Bodineau氏を招聘し、イジングモデルからの巨視的界面の導出に関する最新の結果が紹介された。6では、M.James,S.Pengの両氏を招聘した。7ではエルゴード理論に関する話題が広く討議された。8では、確率論と偏微分方程式論の境界領域を探る試みがなされた。9は確率論全体をカバーする大規模な研究集会であった。特に、2次元イジングモデルのピンニング転移およびランダムウォークの訪問点に関する話題についての連続講演が企画された。上記以外にも外国人研究者の招聘を進め,Bass,Deuschel,Guionnetの3氏を招いた。また分担者の小倉と三苫は海外出張を行い、研究成果の公表につとめた。

研究成果
(40件)

すべてその他

すべて文献書誌 (40件)

[文献書誌] T.Funaki: "Recent results on the Ginzburg-Landau $\nabla \bhi$ interface model."Hydrodynamic Limits and Related Topics,. 71-81 (2000)
[文献書誌] T.Funaki: "Large deviations for the Ginzburg-Landau $\nabla \phi$ interface model."to appear in Probab.Theory Relat.Fields,. (2001)
[文献書誌] T.Funaki: "Fluctuations for $\nabla \phi$ interface model on a wall."to appear in Stoch.Proc.Appl.,. (2001)
[文献書誌] T.Mikami: "Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric."Appl.Math.Optim.. 42. 203-227 (2000)
[文献書誌] M.Takeda: "$L^p$-independence of the spectral radius of symmetric Markov semigroups."Stochastic Processes, Physics and Geometry : New Interplays.. (2000)
[文献書誌] K.Uchiyama: "Uniqueness of solutions to the initial value problem for anintegro-differential equation."Diff.Int.Eoqs.. 13. 401-422 (2000)
[文献書誌] M.Fradon(H.Tanemura): "An infinite system of Brownian balls with infinite range interaction."Stoch.Proc.Appl.. 90. 43-66 (2000)
[文献書誌] H.Osada: "Tagged particles of interacting Brownian motions with skew symmetric drifts."to appear in Monte Carlo Methods and Applications.. (2001)
[文献書誌] Y.Hariya(H.Osada): "Diffusion processes on path spaces with interactions."to appear in Rev.\ Math.\ Phys.. (2001)
[文献書誌] H.Osada: "A family of diffusion processes on Sierpinski carpets."to appear in Probab.Theory Related Fields.. (2001)
[文献書誌] H.Matsumoto: "Quadratic Hamiltonians, Wiener functionals and the metaplectic representations."J.Math.Soc.Japan.,. 52. 269-292 (2000)
[文献書誌] H.Matsumoto: "An analogue of Pitman's $2M-X$ theorem for exponential Wiener functionals, Part I : A time-inversion approach."Nagoya Math.J.. 159. 125-166 (2000)
[文献書誌] K.Uchiyama: "A non-linear evolution equation driven by a logarithmic potential."Bull.London Math.Soc.. 32. 353-363 (2000)
[文献書誌] J.Aaronson(H.Nakada): "Multiple Recurrence of Markov Shifts and Other Infinite Measure Preserving Transformations."Israel Journal of Mathematics,. 117. 285-310 (2000)
[文献書誌] C.Kraaikamp(H.Nakada): "On Normal Numbers for Continued Fractions."Ergodic Theory and Dynamical Systems,. 20. 1405-1421 (2000)
[文献書誌] V.Berthe(H.Nakada): "On Continued Fraction Expansions in Positive Characteristic : Equivalence Relations and Some Metric Propertie"Expositiones Mathematicae,. 18. 257-284 (2000)
[文献書誌] Y.Kasahara: "Large deviation around origin for sums of nonnegative i.i.d.random variables."Nat.Sci.Rep.Ocha.Univ.,. 51. 27-31 (2000)
[文献書誌] M.Katori(H.Tanemura): "Survival probability for discrete time models in one dimension."J.Statist.Phys.. 99. 603-612 (2000)
[文献書誌] Y.Ogura(+富崎松代): "Existence of a strong solution for an integro-differential equation and superposition of diffusion processes."Stochastics in Finite and Infinite Dimensions. 341-359 (2000)
[文献書誌] T.Hara: "The scaling limit of the incipient infinite cluster in high-dimensional percolation.I.Critical exponents."J.Statist.Phys.. 99. 1075-1168 (2000)
[文献書誌] T.Hara: "The scaling limit of the incipient infinite cluster in high-dimensional percolation.II.Integrated super-Brownian excursion."J.Math.Phys.. 41. 1244-1293 (2000)
[文献書誌] K.Kuroda(H.Nagai): "Ergodic type Bellman equation of risk sensitive control and portfolio optimization on infinite time horizon."Optimal Control and Partial Differential Equations,. 530-538 (2001)
[文献書誌] 長井英生: "リスク鋭感的確率制御と数理ファイナンス"システム/制御/情報. 44. 447-454 (2000)
[文献書誌] S.Taniguchi: "L\'evy's stochastic area and the principle of stationary phase."J.Funct.Anal.. 172. 165-176 (2000)
[文献書誌] Y.Ushima: "Certain ratio limit theorem for time inhomogeneous Markov chains."Stochastic Processes, Phisics and Geometry, New Interplays. 28. (2000)
[文献書誌] I.Mitoma: "Infinite level asymptotics of a perturbative Chern-Simons integra Stochastics in Finite and Infinite Dimensions."Birkh\"auser,. 303-319 (2000)
[文献書誌] Y.Ogura(+富崎松代): "Superposition of diffusion processes-Feller Property-."Trends in Probability and related analysis.. 113-128 (1999)
[文献書誌] R.Bass and T.Kumagai: "Laws of the iterated logarithm for some symmetric diffusion processes."Osaka J.Math.,. 37. 625-650 (2000)
[文献書誌] T.Kumagai: "Stochastic processes on fractals and related topics, Sugaku Expositions."Amer.Math.Soc.,. 13. 55-71 (2000)
[文献書誌] H.Kaise(H.Nagai): "Ergodic type Bellman equation of risk-sensitive control."Proceedings ofthe 31st ISCIE International Symposium. 89-94 (2000)
[文献書誌] A.Bensoussan(H.Nagai): "Conditions for no breakdown and bellman equatuins of Risk-sensitive control."Appl.Math.Optim. 42. 91-101 (2000)
[文献書誌] H.Nagai: "Risk-sensitive dynamic asset management with partial information."Stochastics in finite and infinite dimensions,. 321-340 (2000)
[文献書誌] H.Nagai: "Risk-sensitive portfolio optimization with partial information."Proceedings of the 39-th CDC conference,. 1206-1211 (2000)
[文献書誌] C.Donati-Martin(H.Matsumoto): "On positive and negative moments of the integral of geometric Brownian motions."Stat.Prob.Lett.,. 49. 45-52 (2000)
[文献書誌] I.Shigekawa: "The domain of a generator and the intertwining property."Stochastics in Finite and Infinite Dimensions,. 401-410 (2000)
[文献書誌] N.Yoshida: "Application of log-Sobolev inequalitv to the stochastic dynamics of unbounded spin systems on the lattice."J. Funct.Anal.. 173. 74-102 (2000)
[文献書誌] T.Kumagai: "Brownian motion penetrating fractals-An application of the trace theoremof Besov spaces."J.Func.Anal.,. 170. 69-92 (2000)
[文献書誌] G.Ben Arous and T.Kumagai: "Large deviations for Brownian motion on the Sierpinski gasket."Stoch.Proc. Their Appl.,. 85. 225-235 (2000)
[文献書誌] B.M.Hambly,T.Kumagai,S.Kusuoka and X.Y.Zhou: "Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets."J.Math.Soc.Japan,. 52. 373-408 (2000)
[文献書誌] 舟木直久: "確率微分方程式(第2版)"岩波書店. 203 (2000)

2000 年度 実績報告書

確率論の総合的研究

研究代表者

舟木 直久 東京大学, 大学院・数理科学研究科, 教授 (60112174)

研究成果

[文献書誌] T.Funaki: "Recent results on the Ginzburg-Landau $\nabla \bhi$ interface model."Hydrodynamic Limits and Related Topics,. 71-81 (2000)

[文献書誌] T.Funaki: "Large deviations for the Ginzburg-Landau $\nabla \phi$ interface model."to appear in Probab.Theory Relat.Fields,. (2001)

[文献書誌] T.Funaki: "Fluctuations for $\nabla \phi$ interface model on a wall."to appear in Stoch.Proc.Appl.,. (2001)

[文献書誌] T.Mikami: "Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric."Appl.Math.Optim.. 42. 203-227 (2000)

[文献書誌] M.Takeda: "$L^p$-independence of the spectral radius of symmetric Markov semigroups."Stochastic Processes, Physics and Geometry : New Interplays.. (2000)

[文献書誌] K.Uchiyama: "Uniqueness of solutions to the initial value problem for anintegro-differential equation."Diff.Int.Eoqs.. 13. 401-422 (2000)

[文献書誌] M.Fradon(H.Tanemura): "An infinite system of Brownian balls with infinite range interaction."Stoch.Proc.Appl.. 90. 43-66 (2000)

[文献書誌] H.Osada: "Tagged particles of interacting Brownian motions with skew symmetric drifts."to appear in Monte Carlo Methods and Applications.. (2001)

[文献書誌] Y.Hariya(H.Osada): "Diffusion processes on path spaces with interactions."to appear in Rev.\ Math.\ Phys.. (2001)

[文献書誌] H.Osada: "A family of diffusion processes on Sierpinski carpets."to appear in Probab.Theory Related Fields.. (2001)

[文献書誌] H.Matsumoto: "Quadratic Hamiltonians, Wiener functionals and the metaplectic representations."J.Math.Soc.Japan.,. 52. 269-292 (2000)

[文献書誌] H.Matsumoto: "An analogue of Pitman's $2M-X$ theorem for exponential Wiener functionals, Part I : A time-inversion approach."Nagoya Math.J.. 159. 125-166 (2000)

[文献書誌] K.Uchiyama: "A non-linear evolution equation driven by a logarithmic potential."Bull.London Math.Soc.. 32. 353-363 (2000)

[文献書誌] J.Aaronson(H.Nakada): "Multiple Recurrence of Markov Shifts and Other Infinite Measure Preserving Transformations."Israel Journal of Mathematics,. 117. 285-310 (2000)

[文献書誌] C.Kraaikamp(H.Nakada): "On Normal Numbers for Continued Fractions."Ergodic Theory and Dynamical Systems,. 20. 1405-1421 (2000)

[文献書誌] V.Berthe(H.Nakada): "On Continued Fraction Expansions in Positive Characteristic : Equivalence Relations and Some Metric Propertie"Expositiones Mathematicae,. 18. 257-284 (2000)

[文献書誌] Y.Kasahara: "Large deviation around origin for sums of nonnegative i.i.d.random variables."Nat.Sci.Rep.Ocha.Univ.,. 51. 27-31 (2000)

[文献書誌] M.Katori(H.Tanemura): "Survival probability for discrete time models in one dimension."J.Statist.Phys.. 99. 603-612 (2000)

[文献書誌] Y.Ogura(+富崎松代): "Existence of a strong solution for an integro-differential equation and superposition of diffusion processes."Stochastics in Finite and Infinite Dimensions. 341-359 (2000)

[文献書誌] T.Hara: "The scaling limit of the incipient infinite cluster in high-dimensional percolation.I.Critical exponents."J.Statist.Phys.. 99. 1075-1168 (2000)

[文献書誌] T.Hara: "The scaling limit of the incipient infinite cluster in high-dimensional percolation.II.Integrated super-Brownian excursion."J.Math.Phys.. 41. 1244-1293 (2000)

[文献書誌] K.Kuroda(H.Nagai): "Ergodic type Bellman equation of risk sensitive control and portfolio optimization on infinite time horizon."Optimal Control and Partial Differential Equations,. 530-538 (2001)

[文献書誌] 長井英生: "リスク鋭感的確率制御と数理ファイナンス"システム/制御/情報. 44. 447-454 (2000)

[文献書誌] S.Taniguchi: "L\'evy's stochastic area and the principle of stationary phase."J.Funct.Anal.. 172. 165-176 (2000)

[文献書誌] Y.Ushima: "Certain ratio limit theorem for time inhomogeneous Markov chains."Stochastic Processes, Phisics and Geometry, New Interplays. 28. (2000)

[文献書誌] I.Mitoma: "Infinite level asymptotics of a perturbative Chern-Simons integra Stochastics in Finite and Infinite Dimensions."Birkh\"auser,. 303-319 (2000)

[文献書誌] Y.Ogura(+富崎松代): "Superposition of diffusion processes-Feller Property-."Trends in Probability and related analysis.. 113-128 (1999)

[文献書誌] R.Bass and T.Kumagai: "Laws of the iterated logarithm for some symmetric diffusion processes."Osaka J.Math.,. 37. 625-650 (2000)

[文献書誌] T.Kumagai: "Stochastic processes on fractals and related topics, Sugaku Expositions."Amer.Math.Soc.,. 13. 55-71 (2000)

[文献書誌] H.Kaise(H.Nagai): "Ergodic type Bellman equation of risk-sensitive control."Proceedings ofthe 31st ISCIE International Symposium. 89-94 (2000)

[文献書誌] A.Bensoussan(H.Nagai): "Conditions for no breakdown and bellman equatuins of Risk-sensitive control."Appl.Math.Optim. 42. 91-101 (2000)

[文献書誌] H.Nagai: "Risk-sensitive dynamic asset management with partial information."Stochastics in finite and infinite dimensions,. 321-340 (2000)

[文献書誌] H.Nagai: "Risk-sensitive portfolio optimization with partial information."Proceedings of the 39-th CDC conference,. 1206-1211 (2000)

[文献書誌] C.Donati-Martin(H.Matsumoto): "On positive and negative moments of the integral of geometric Brownian motions."Stat.Prob.Lett.,. 49. 45-52 (2000)

[文献書誌] I.Shigekawa: "The domain of a generator and the intertwining property."Stochastics in Finite and Infinite Dimensions,. 401-410 (2000)

[文献書誌] N.Yoshida: "Application of log-Sobolev inequalitv to the stochastic dynamics of unbounded spin systems on the lattice."J. Funct.Anal.. 173. 74-102 (2000)

[文献書誌] T.Kumagai: "Brownian motion penetrating fractals-An application of the trace theoremof Besov spaces."J.Func.Anal.,. 170. 69-92 (2000)

[文献書誌] G.Ben Arous and T.Kumagai: "Large deviations for Brownian motion on the Sierpinski gasket."Stoch.Proc. Their Appl.,. 85. 225-235 (2000)

[文献書誌] B.M.Hambly,T.Kumagai,S.Kusuoka and X.Y.Zhou: "Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets."J.Math.Soc.Japan,. 52. 373-408 (2000)

[文献書誌] 舟木直久: "確率微分方程式(第2版)"岩波書店. 203 (2000)

2000 年度実績報告書

舟木直久東京大学, 大学院・数理科学研究科, 教授 (60112174)