1999 Fiscal Year Annual Research Report

確率論の総合的研究

Research Project

Project/Area Number	11304003
Research Category	Grant-in-Aid for Scientific Research (A)
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, 大学院・理学研究科, 教授 (00127234) 内山耕平東京工業大学, 大学院・理工学研究科, 教授 (00117566) 竹田雅好東北大学, 大学院・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, 大学院・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5回開催した. 1.Markov processes and related analysis(マルコフ過程と関連した解析) 2.流体力学極限秋の学校 3.ランダム行列とその周辺 4.確率解析とその応用 5.エルゴード理論の展望である.1 では P.J.Fitzsimmons 教授を招聘し最近のマルコフ過程についての多くの研究成果が発表され,同教授との議論を通して種々の領域における反射壁過程の半マルチンゲール性の統一的取り扱いに関する方向性が得られた.2 では界面モデル・格子気体・確率偏微分方程式・自由確率等に関する報告があり,その後の研究によって壁上の界面モデル・大偏差原理に関する新たな知見が得られた.3 ではランダム行列・アンダーソン局在・量子カオス等に関する講演があり,講演の内容をまとめた報告集を作成した.4 では確率振動積分の慚近挙動・ループ空間上の対数ソボレフ不等式・上半平面上のブラウン運動とマースラプラシアン・汎関数積分と跡公式に関する報告があった.5 では K.Schmidt教授を招きエルゴード理論に関する数多くの成果が公表された.またβ-シフトに関する新たな研究の方向性が見つかった. 上記以外にも外国人研究者の招聘を進め,R.Roy 教授による無限個のボールの配置に基づく連続パーコレーション模型・バックベンドのあるパーコレーション模型,A.Kohatsu-Higa 教授による確率微分方程式の数値解析,D.loffe 教授の相転移の下での界面の解析と Wulff 形態の出現に関する報告があった.これら3教授の招聘を通して,それぞれ,ポアソン棒モデルの連続パーコレーション,確率微分方程式の Euler-丸山スキームによる弱近似解の収束性,相互作用のあるブラウン運動系の零温度極限についての成果が得られた.なお、研究代表者の舟木は海外出張を行い界面モデル等に関する研究成果の公表に努めた.

Research Products
(39 results)

All Other

All Publications (39 results)

[Publications] T. Funaki: "Free boundary problem from stochastic lattice gas model"Ann. Inst. Henri Poincar\' e. 35. 573-603 (1999)
[Publications] T. Funaki: "Singular limit for stochastic reaction-diffusion equation and generation of random interfaces"Acta Mathematica Sinica, English Series. 15. 407-438 (1999)
[Publications] T. Funaki: "Recent results on the Ginzburg-Landau $\nabla \phi$ interface model.to appear in Proceedings of the Workshop on "Hydrodynamic Limits""Fields Institute Communications and Monograph Series. (2000)
[Publications] P. Biler (T. Funaki): "Interacting jump Markov processes associated with nonlocal quadratic evolution problems"Probability and Mathematical Statistics. (2000)
[Publications] T.Mikami: "Markov marginal problems and their applications to Markov optimal control"Stochastic Analysis, Control, Optimization and Applications. 457-476 (1999)
[Publications] Takeda Masayoshi: "Exponential decay of lifetime and a Theorem of Kac on total occupation times"Potential Anal.. 11. 235-247 (1999)
[Publications] Takeda Masayoshi: "Topics on Dirichlet forms and symmetric Markov processes"Sugaku Expositions. 12. 201-222 (1999)
[Publications] Fukushima, Masatoshi (M. Takeda): "Large deviations and LIL's for Brownian motlons on nested fractals"Osaka J.Math.. (2000)
[Publications] Takeda Masayoshi: "$L p$-independence of the spectral radius of symmetric Markov processes"Proceedings of "International Conference on Infinite Dimensional (Stochastic) Analysis and Quantum Physics". (2000)
[Publications] 南就将: "Level statistics for quantum Hamiltonians--Some preliminary ideas toward mathematical justification of the theory of Berry and Tabor"Proceedings of the Second Congress ISAAC. (2000)
[Publications] N. Minami: "On the Poisson limit theorems of Sinai and Major"Communications in Mathematical Physics. (2000)
[Publications] K. Uchiyama: "Uniqueness of solutions to the initial value problem for an integro-differential equation"Diff. Int. Eqs.. (2000)
[Publications] K. Uchiyama: "A non-linear evolution equation driven by a logarithmic potential"Bull. London Math. Soc.. (2000)
[Publications] Y. Kasahara: "On tail probability of local times of Gaussian processes"Stoch. Proc. Appl.. 82. 15-21 (1999)
[Publications] Y. Kasahara: "A note on the Local Time of Fractional Brownian Motion"J. Theoret. Probab.. 12. 207-216 (1999)
[Publications] Y. Kasahara: "Tail probability of local times of Gaussian processes and diffusions"Probability and Related Analysi eds. N. Kono & N. R. Shieh, World Scientific. 239-248 (1999)
[Publications] 仲田均: "Multple Recurrence of Markov Shifts and Other Infinite Measure Preserving Transformations"Israel Journal of Mathematics. (2000)
[Publications] 種村秀紀: "Survival probability for discrete time model in one dimension"Journal of Statistical Physics. (2000)
[Publications] N. Ikeda (H. Matsumoto): "Brownian motion on the Hyperbolic plane and Selberg trace formula"J. Func. Anal.. 163. 63-110 (1999)
[Publications] H. Matsumoto: "A version of Pitman' s $2M-X$ theorem for geometric Brownian motions"C. R. Acad. Sci. Paris. 328. 1067-1074 (1999)
[Publications] H. Matsumoto: "Some change of probabilities related to a geometric brownian motion version of Pitman' s $2M-X$ theorem"Elect. Comm. Prob.. 4. 15-23 (1999)
[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.. (2000)
[Publications] H. Matsumoto: "An analogue of Pitman' s $2M-X$ theorem for exponential Wiener functionals, Part II : the role of generalized inverse Gaussian distributions"Nagoya Math. J.. (2000)
[Publications] C. Donati-Martin (H. Matsumoto): "On positive and negative moments of the integral of geometric Brownian motions"Stat. Prob. Lett.. (2000)
[Publications] I.. Shigekawa: "Semigroup domination on a Riemannian manifold with boundary"special volume of Takeyuki Hida. (2000)
[Publications] H. Nagai: "Singular Limits of bellman Equations of Ergodic Type Related to Risk-Sensitive Control"Stochastic Analysis, Control, Optimization and Applications, a volume in honor of W. H. Fleming. 95-114 (1999)
[Publications] A. Bensoussan (H. Nagai): "Conditions for no breakdown and Bellman equations of risk sensitive control"Applied Math. Optim.. (2000)
[Publications] H. Kaise (H. Nagai): "Ergodic Type Bellman equations of risk-sensitive control with large parameters and their singular limits"Asymptotic Analysis. 20. 279-299 (1999)
[Publications] Y. Ogura (M. Tomisaki): "Superposition of diffusion processes -- Feller Property --"Treds in Probability and related analysis. 113-128 (1999)
[Publications] H. O. Georgii (Y. Higuchi): "Percolation and number of phases in the 2D lsing model"J. Math. Phys.. (2000)
[Publications] Y. Higuchi: "On the speed of convergence for two dimensional first-passage lsing percolation"Annals of Probability. (2000)
[Publications] H. Sugita (S. Taniguchi): "A remark on stochastic oscillatory integrals with respect to a pinned Wiener measure"Kyushu Journal of Mathematics. 53. 151-162 (1999)
[Publications] S. Taniguchi: "Stochastic oscillatory integrals with quadratic phase function and Jacobi equation"Probability Theory and Related Fields. 114. 291-308 (1999)
[Publications] S. Taniguchi: "L\' evy' s stochastic area and the principle of stationary Phase"Journal of Functional Analysis. (2000)
[Publications] I. Mitoma: "One loop approximation of the Chern-Simons integral"the volume in honor of 70th birthday of T. Hida. (2000)
[Publications] I. Mitoma: "Wiener space approach to a perturbative Chern-Simons integral"Stochastic-Processes, Physics and Geometry, New Interplays Proceedings, Canad. Math. Soc.. (2000)
[Publications] Y. Oshima: "Certain ratio limit theorem for time inhomogeneous Markov chains"Stochastic Processes, Physics and Geometry : New Interplays A volume in Honor of Sergio Albeverio. (2000)
[Publications] 長井英生: "確率微分方程式"共立出版. 227 (1999)

1999 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: "Free boundary problem from stochastic lattice gas model"Ann. Inst. Henri Poincar\' e. 35. 573-603 (1999)

[Publications] T. Funaki: "Singular limit for stochastic reaction-diffusion equation and generation of random interfaces"Acta Mathematica Sinica, English Series. 15. 407-438 (1999)

[Publications] T. Funaki: "Recent results on the Ginzburg-Landau $\nabla \phi$ interface model.to appear in Proceedings of the Workshop on "Hydrodynamic Limits""Fields Institute Communications and Monograph Series. (2000)

[Publications] P. Biler (T. Funaki): "Interacting jump Markov processes associated with nonlocal quadratic evolution problems"Probability and Mathematical Statistics. (2000)

[Publications] T.Mikami: "Markov marginal problems and their applications to Markov optimal control"Stochastic Analysis, Control, Optimization and Applications. 457-476 (1999)

[Publications] Takeda Masayoshi: "Exponential decay of lifetime and a Theorem of Kac on total occupation times"Potential Anal.. 11. 235-247 (1999)

[Publications] Takeda Masayoshi: "Topics on Dirichlet forms and symmetric Markov processes"Sugaku Expositions. 12. 201-222 (1999)

[Publications] Fukushima, Masatoshi (M. Takeda): "Large deviations and LIL's for Brownian motlons on nested fractals"Osaka J.Math.. (2000)

[Publications] Takeda Masayoshi: "$L p$-independence of the spectral radius of symmetric Markov processes"Proceedings of "International Conference on Infinite Dimensional (Stochastic) Analysis and Quantum Physics". (2000)

[Publications] 南 就将: "Level statistics for quantum Hamiltonians--Some preliminary ideas toward mathematical justification of the theory of Berry and Tabor"Proceedings of the Second Congress ISAAC. (2000)

[Publications] N. Minami: "On the Poisson limit theorems of Sinai and Major"Communications in Mathematical Physics. (2000)

[Publications] K. Uchiyama: "Uniqueness of solutions to the initial value problem for an integro-differential equation"Diff. Int. Eqs.. (2000)

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

[Publications] Y. Kasahara: "On tail probability of local times of Gaussian processes"Stoch. Proc. Appl.. 82. 15-21 (1999)

[Publications] Y. Kasahara: "A note on the Local Time of Fractional Brownian Motion"J. Theoret. Probab.. 12. 207-216 (1999)

[Publications] Y. Kasahara: "Tail probability of local times of Gaussian processes and diffusions"Probability and Related Analysi eds. N. Kono & N. R. Shieh, World Scientific. 239-248 (1999)

[Publications] 仲田 均: "Multple Recurrence of Markov Shifts and Other Infinite Measure Preserving Transformations"Israel Journal of Mathematics. (2000)

[Publications] 種村秀紀: "Survival probability for discrete time model in one dimension"Journal of Statistical Physics. (2000)

[Publications] N. Ikeda (H. Matsumoto): "Brownian motion on the Hyperbolic plane and Selberg trace formula"J. Func. Anal.. 163. 63-110 (1999)

[Publications] H. Matsumoto: "A version of Pitman' s $2M-X$ theorem for geometric Brownian motions"C. R. Acad. Sci. Paris. 328. 1067-1074 (1999)

[Publications] H. Matsumoto: "Some change of probabilities related to a geometric brownian motion version of Pitman' s $2M-X$ theorem"Elect. Comm. Prob.. 4. 15-23 (1999)

[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.. (2000)

[Publications] H. Matsumoto: "An analogue of Pitman' s $2M-X$ theorem for exponential Wiener functionals, Part II : the role of generalized inverse Gaussian distributions"Nagoya Math. J.. (2000)

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

[Publications] I.. Shigekawa: "Semigroup domination on a Riemannian manifold with boundary"special volume of Takeyuki Hida. (2000)

[Publications] H. Nagai: "Singular Limits of bellman Equations of Ergodic Type Related to Risk-Sensitive Control"Stochastic Analysis, Control, Optimization and Applications, a volume in honor of W. H. Fleming. 95-114 (1999)

[Publications] A. Bensoussan (H. Nagai): "Conditions for no breakdown and Bellman equations of risk sensitive control"Applied Math. Optim.. (2000)

[Publications] H. Kaise (H. Nagai): "Ergodic Type Bellman equations of risk-sensitive control with large parameters and their singular limits"Asymptotic Analysis. 20. 279-299 (1999)

[Publications] Y. Ogura (M. Tomisaki): "Superposition of diffusion processes -- Feller Property --"Treds in Probability and related analysis. 113-128 (1999)

[Publications] H. O. Georgii (Y. Higuchi): "Percolation and number of phases in the 2D lsing model"J. Math. Phys.. (2000)

[Publications] Y. Higuchi: "On the speed of convergence for two dimensional first-passage lsing percolation"Annals of Probability. (2000)

[Publications] H. Sugita (S. Taniguchi): "A remark on stochastic oscillatory integrals with respect to a pinned Wiener measure"Kyushu Journal of Mathematics. 53. 151-162 (1999)

[Publications] S. Taniguchi: "Stochastic oscillatory integrals with quadratic phase function and Jacobi equation"Probability Theory and Related Fields. 114. 291-308 (1999)

[Publications] S. Taniguchi: "L\' evy' s stochastic area and the principle of stationary Phase"Journal of Functional Analysis. (2000)

[Publications] I. Mitoma: "One loop approximation of the Chern-Simons integral"the volume in honor of 70th birthday of T. Hida. (2000)

[Publications] I. Mitoma: "Wiener space approach to a perturbative Chern-Simons integral"Stochastic-Processes, Physics and Geometry, New Interplays Proceedings, Canad. Math. Soc.. (2000)

[Publications] Y. Oshima: "Certain ratio limit theorem for time inhomogeneous Markov chains"Stochastic Processes, Physics and Geometry : New Interplays A volume in Honor of Sergio Albeverio. (2000)

[Publications] 長井 英生: "確率微分方程式"共立出版. 227 (1999)

舟木直久東京大学, 大学院・数理科学研究科, 教授 (60112174)

[Publications] 南就将: "Level statistics for quantum Hamiltonians--Some preliminary ideas toward mathematical justification of the theory of Berry and Tabor"Proceedings of the Second Congress ISAAC. (2000)

[Publications] 仲田均: "Multple Recurrence of Markov Shifts and Other Infinite Measure Preserving Transformations"Israel Journal of Mathematics. (2000)

[Publications] 長井英生: "確率微分方程式"共立出版. 227 (1999)