2000 Fiscal Year Annual Research Report

確率論の総合的研究

Research Project

Project/Area Number	11304003
Research Institution	The University of Tokyo
Principal Investigator	舟木直久東京大学, 大学院・数理科学研究科, 教授 (60112174)
Co-Investigator(Kenkyū-buntansha)	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)
Keywords	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
Research Abstract	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。

Research Products
(40 results)

All Other

All Publications (40 results)

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

2000 Fiscal Year Annual Research Report

確率論の総合的研究

Principal Investigator

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

Research Products

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

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

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

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

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

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

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

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

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

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

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

[Publications] 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)

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

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

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

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

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

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

[Publications] 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)

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

[Publications] 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)

[Publications] 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)

[Publications] 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)

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

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

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

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

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

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

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

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

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

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

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

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

[Publications] 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)

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

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

[Publications] 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)

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

舟木直久東京大学, 大学院・数理科学研究科, 教授 (60112174)