2000 Fiscal Year Annual Research Report

平衡確率現象の総合的研究

Research Project

Project/Area Number	10304006
Research Institution	Hiroshima University
Principal Investigator	久保泉広島大学, 大学院・理学研究科, 教授 (70022621)
Co-Investigator(Kenkyū-buntansha)	前島信慶応大学, 理工学部, 教授 (90051846) 岡部靖憲東京大学, 大学院・工学研究科, 教授 (30028211) 舟木直久東京大学, 大学院・数理科学研究科, 教授 (60112174) 会田茂樹大阪大学, 大学院・基礎工学研究科, 助教授 (90222455) 尾畑伸明名古屋大学, 大学院・多元数理科学研究科, 助教授 (10169360)
Keywords	確率解析 / 無限次元解析 / 白色雑音解析 / 情報解析 / 非線形解析 / 量子解析 / 力学系 / 自己相似過程
Research Abstract	確率現象の多くは、ある種の変換に関する平衡現象として捉らえられるが、その観点からの総合的研究を目指し、9つの研究集会を開催した。キーワードに沿って、幾つかの成果を説明する。 1.確率解析:会田は、ループ空間上の熱核に関する解析、特に対数ソボレフ不等式、クラーク・オコーン公式の詳細な研究成果を得た。この結果はメキシコで開催された国際会議において発表された。 2.非線形解析と確率解析:舟木は、界面モデルに対する流体力学極限を考え,巨視的な界面方程式としてある非線形偏微分方程式が得られることを大数の法則として定式化し、さらに大偏差原理を考察した。平良は、準線形楕円型方程式や反応拡散方程式等の非線形偏微分方程式の境界値問題をブラウン運動を通して研究し、非線型弾性体力学・反応速度論・人口動態論・山辺の問題などを解明した。 3.白色雑音解析:久保・尾畑を中心とし、白色雑音を記述する空間の構成法と特徴付けが非常に一般的にかつ明快に提示されるようになり、またそこでの作用素のシンボルによる特徴付けがさらに進展した。それらの結果は、久保により、インド統計研究所で開催された国際会議で発表された。 4.情報解析:井原は、最も一般的な設定の下でフィードバックのあるガウス型通信路を考え、通信路を通して送られる相互情報量に対する一般公式を導き、さらに、大偏差定理の情報理論への種々の応用や定常無記憶ガウス型情報源に対し与えられた誤り指数に対する最小符号化レートを求めた。岡部は、揺動散逸定理を指導原理として提唱してきた解析方法における各種のテストの統合化システムを開発した。また、計量ベクトル空間内の流れに対するKM_2O-ランジュヴァン方程式論を構築し、その応用を調べた。 5.自己相似過程:竹中は、SαS-過程が有限次元分布により決定されると言う決定性を示した。前島は、「半自己分解可能分布」の概念を導入し、半自己相似確率過程や作用素的半自己分解可能分布へ拡張し詳細な研究を行った。また、決定性はこのクラスが限界であるとの知見も得た。その他の分担者を中心とした研究も多くなされたが、詳しくは業績リストを参照されたい。

Research Products
(45 results)

All Other

All Publications (45 results)

[Publications] Nobuhiro Asai: "Bell numbers, log-concavity, and log-convexity"Acta Appl.Math.. (in press). (2001)
[Publications] Nobuhiro Asai: "General characterization theorems and intrinsic topologies in white noise analysis"Hiroshima Math,J.. (in press). (2001)
[Publications] Nobuhiro Asai: "Roles of Log-concavity, log-convexity, and growth order in white noise analysis"Infinite Dimensional Analysis and Quantum Probability. 4. 1-27 (2001)
[Publications] Nobuhiro Asai: "Characterization of test functions in CKS-space"Mathematical Physics and Stochastic Analysis. 68-78 (2000)
[Publications] Nobuhiro Asai: "CKS-space in terms of growth functions"Quantum Information II. 17-27 (2000)
[Publications] Nobuhiro Asai: "Characterization of Hida measures in white noise analysis"Infinite Dimensional Harmonic Analysis. 70-83 (2000)
[Publications] Nobuhiro Asai: "Feynman integrals associated with Albeverio-Hoegh-Krohn and Laplace transform potentials"Stochastics in Finite and Infinite Dimensions. 29-48 (2000)
[Publications] Kazuaki Taira: "Feller semigroups and degenerate elliptic operators with Ventcel 'boundary Conditions"Studia Matematica. 144(in press). (2001)
[Publications] Kazuaki Taira: "Positive solutions of diffusive logistic equations"Taiwanese Journal of Mathematics. 5. 1-24 (2001)
[Publications] Kazuaki Taira: "Feller semigroups generated by degenerate elliptic operators II"The Proceedings of the First International Conference on Semigroups of Operators. 304-319 (2001)
[Publications] Kazuaki Taira: "A degenerate Neumann problem for quasilinear elliptic equations"Tokyo Journal of Methematics. 23. 227-234 (2000)
[Publications] Kazuaki Taira: "Stability in chemical reactor theory"Proceedings of the Sixth International Conference on Evolution Equations and their Applications in Physical and Life Sciences. 421-433 (2000)
[Publications] Kazuaki Taira: "Feller semigroups generated by degenerate elliptic operators"Semigroup Forum. 60. 296-309 (2000)
[Publications] K.Umezu: "Positive solutions of semilinear elliptic boundary value problems in chemical reactor theory"The Proceedings of the International Society for Analysis, Applications and Computation '97 Congress. 415-422 (2000)
[Publications] Tadahisa Funaki: "Fluctuations for ▽φ interface model on a wall"Stoch.Proc.Appl.. (in press). (2001)
[Publications] Tadahisa Funaki: "Large deviations for the Ginzburg-Landau ▽φ interface model."Probab.Theory Relat.Fields. 20(in press). (2001)
[Publications] Tadahisa Funaki: "Recent results on the Ginzburg-Landau ▽φ interface model"Hydrodynamic Limits and Related Topics. 71-81 (2000)
[Publications] Makoto Maejima: "Completely operator semi-selfdecomposable distribuitons"Tokyo J.Math.. 395-253 (2000)
[Publications] Makoto Maejima: "Distributions of selfsimilar and semi-selfsimilar processes with independent increments"Statist.Probab.Lett.. 47. 395-401 (2000)
[Publications] Shunsuke Ihara: "Large deviation theorems for Gaussian processes and their applications in information theory"Acta Applicande Math.. (in press). (2001)
[Publications] Shunsuke Ihara: "Error exponent for coding of memoryless Gaussian sources with a fidelity criterion"IEICE Trans.Fundamentals. E83-A. 1891-1897 (2000)
[Publications] Nobuaki Obata: "Quadratic quantum white noises and Levy Laplacian"Nonliner Analysis. (in press). (2001)
[Publications] Y.Hashimoto: "A quantum aspect of asymptotic spectral analysis of large Hamming graphs"in "Quantum Information III". (in press). (2001)
[Publications] Nobuaki Obata: "White noise operator theory : Fundamental concepts and developing applications"Proceedings of Volterra International School. (in press). (2001)
[Publications] Nobuaki Obata: "Coherent state representation and unitarity condition in white noise calculus"J.Korean Math.Soc.. 38(in press). (2001)
[Publications] Nobuaki Obata: "Coherent state representations in white noise calculus"Can.Math.Soc.Proceedings Series. (in press). (2001)
[Publications] Nobuaki Obata: "Complex white noise and coherent state representation"Acta Appl.Math.. (in press). (2001)
[Publications] Nobuaki Obata: "A note on coherent state representations of white noise operators"Quantum Information II. 135-147 (2000)
[Publications] U.C.Ji: "Initial value problem for white noise operators and quantum stochastic processes"Infinite Dimensional Harmonic Analysis. 203-216 (2000)
[Publications] D.M.Chung: "Normal-ordered white noise differential equations I : Existence of solutions as Fock space operators"Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability. 115-135 (2000)
[Publications] K.Oosawa: "Colour-coding reveals tandem repeats in the Escherichia coli genome"J.Mol.Biology. 298. 343-349 (2000)
[Publications] Shigeki Aida: "An estimate of the gap of spectrum of Schroedinger operators which generate hyperbounded semigroups"J.Funct.Anal.. (in press). (2001)
[Publications] Shigeki Aida: "On the short time asymptotics of transition probability of diffusion on path groups"in "Potential Analysis". (in press). (2001)
[Publications] Shigeki Aida: "Short time asymptotics of certain infinite dimensional diffusion processes"The Proceedings of 7th Workshop on stochastic analysis and related topics, Progress in Probability. (in press). (2001)
[Publications] Shigeki Aida: "On the irreducibility of the Dirichlet forms in infinite dimensional spaces"Osaka J.Math.. (in press). (2001)
[Publications] Shigeki Aida: "Precise Gaussian lower bounds on heat kernels"Stochastics in Finite and Infinite Dimensions. 1-28 (2000)
[Publications] Shigeki Aida: "Stochastic analysis on loop spaces"Sugaku expositions. 13. 197-214 (2000)
[Publications] Shigeki Aida: "Equivalence of heat kernel measure and pinned Wiener measure on loop groups"C.R.Acad.Sci.Paris,. 331. 709-712 (2000)
[Publications] Shigeki Aida: "Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces"J.Funct.Anal.. 174. 430-477 (2000)
[Publications] Keizo Takashima: "Random walk tests and Pseudorandom number generators"Proceedings of International Conference of Mathematical Analysis and Applications, Gyeongsang National Univ.. (in press). (2001)
[Publications] Keizo Takashima: "Hybrid pseudo-random number generation"Monte Carlo Methods and Applications. 6. 49-59 (2000)
[Publications] M.Denker: "Sierpinski gasket as a Martin boundary I"Potential Analysis. (in press). (2001)
[Publications] A.Danilenko: "On measure theoretical analogue of the Takesaki structure theorem for type III factors"Colloquim Mathematicum. 84/85. 485-493 (2000)
[Publications] Toshihiro Hamachi: "On nonsingular Chacon transformations"Illinois Journal Math.. 44. 1-16 (2000)
[Publications] Toshihiro Hamachi: "Canonical subrelations of ergodic equivalence relation-subrelations"Journal of Operator Theory. 43. 3-34 (2000)

2000 Fiscal Year Annual Research Report

平衡確率現象の総合的研究

Principal Investigator

久保 泉 広島大学, 大学院・理学研究科, 教授 (70022621)

Research Products

[Publications] Nobuhiro Asai: "Bell numbers, log-concavity, and log-convexity"Acta Appl.Math.. (in press). (2001)

[Publications] Nobuhiro Asai: "General characterization theorems and intrinsic topologies in white noise analysis"Hiroshima Math,J.. (in press). (2001)

[Publications] Nobuhiro Asai: "Roles of Log-concavity, log-convexity, and growth order in white noise analysis"Infinite Dimensional Analysis and Quantum Probability. 4. 1-27 (2001)

[Publications] Nobuhiro Asai: "Characterization of test functions in CKS-space"Mathematical Physics and Stochastic Analysis. 68-78 (2000)

[Publications] Nobuhiro Asai: "CKS-space in terms of growth functions"Quantum Information II. 17-27 (2000)

[Publications] Nobuhiro Asai: "Characterization of Hida measures in white noise analysis"Infinite Dimensional Harmonic Analysis. 70-83 (2000)

[Publications] Nobuhiro Asai: "Feynman integrals associated with Albeverio-Hoegh-Krohn and Laplace transform potentials"Stochastics in Finite and Infinite Dimensions. 29-48 (2000)

[Publications] Kazuaki Taira: "Feller semigroups and degenerate elliptic operators with Ventcel 'boundary Conditions"Studia Matematica. 144(in press). (2001)

[Publications] Kazuaki Taira: "Positive solutions of diffusive logistic equations"Taiwanese Journal of Mathematics. 5. 1-24 (2001)

[Publications] Kazuaki Taira: "Feller semigroups generated by degenerate elliptic operators II"The Proceedings of the First International Conference on Semigroups of Operators. 304-319 (2001)

[Publications] Kazuaki Taira: "A degenerate Neumann problem for quasilinear elliptic equations"Tokyo Journal of Methematics. 23. 227-234 (2000)

[Publications] Kazuaki Taira: "Stability in chemical reactor theory"Proceedings of the Sixth International Conference on Evolution Equations and their Applications in Physical and Life Sciences. 421-433 (2000)

[Publications] Kazuaki Taira: "Feller semigroups generated by degenerate elliptic operators"Semigroup Forum. 60. 296-309 (2000)

[Publications] K.Umezu: "Positive solutions of semilinear elliptic boundary value problems in chemical reactor theory"The Proceedings of the International Society for Analysis, Applications and Computation '97 Congress. 415-422 (2000)

[Publications] Tadahisa Funaki: "Fluctuations for ▽φ interface model on a wall"Stoch.Proc.Appl.. (in press). (2001)

[Publications] Tadahisa Funaki: "Large deviations for the Ginzburg-Landau ▽φ interface model."Probab.Theory Relat.Fields. 20(in press). (2001)

[Publications] Tadahisa Funaki: "Recent results on the Ginzburg-Landau ▽φ interface model"Hydrodynamic Limits and Related Topics. 71-81 (2000)

[Publications] Makoto Maejima: "Completely operator semi-selfdecomposable distribuitons"Tokyo J.Math.. 395-253 (2000)

[Publications] Makoto Maejima: "Distributions of selfsimilar and semi-selfsimilar processes with independent increments"Statist.Probab.Lett.. 47. 395-401 (2000)

[Publications] Shunsuke Ihara: "Large deviation theorems for Gaussian processes and their applications in information theory"Acta Applicande Math.. (in press). (2001)

[Publications] Shunsuke Ihara: "Error exponent for coding of memoryless Gaussian sources with a fidelity criterion"IEICE Trans.Fundamentals. E83-A. 1891-1897 (2000)

[Publications] Nobuaki Obata: "Quadratic quantum white noises and Levy Laplacian"Nonliner Analysis. (in press). (2001)

[Publications] Y.Hashimoto: "A quantum aspect of asymptotic spectral analysis of large Hamming graphs"in "Quantum Information III". (in press). (2001)

[Publications] Nobuaki Obata: "White noise operator theory : Fundamental concepts and developing applications"Proceedings of Volterra International School. (in press). (2001)

[Publications] Nobuaki Obata: "Coherent state representation and unitarity condition in white noise calculus"J.Korean Math.Soc.. 38(in press). (2001)

[Publications] Nobuaki Obata: "Coherent state representations in white noise calculus"Can.Math.Soc.Proceedings Series. (in press). (2001)

[Publications] Nobuaki Obata: "Complex white noise and coherent state representation"Acta Appl.Math.. (in press). (2001)

[Publications] Nobuaki Obata: "A note on coherent state representations of white noise operators"Quantum Information II. 135-147 (2000)

[Publications] U.C.Ji: "Initial value problem for white noise operators and quantum stochastic processes"Infinite Dimensional Harmonic Analysis. 203-216 (2000)

[Publications] D.M.Chung: "Normal-ordered white noise differential equations I : Existence of solutions as Fock space operators"Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability. 115-135 (2000)

[Publications] K.Oosawa: "Colour-coding reveals tandem repeats in the Escherichia coli genome"J.Mol.Biology. 298. 343-349 (2000)

[Publications] Shigeki Aida: "An estimate of the gap of spectrum of Schroedinger operators which generate hyperbounded semigroups"J.Funct.Anal.. (in press). (2001)

[Publications] Shigeki Aida: "On the short time asymptotics of transition probability of diffusion on path groups"in "Potential Analysis". (in press). (2001)

[Publications] Shigeki Aida: "Short time asymptotics of certain infinite dimensional diffusion processes"The Proceedings of 7th Workshop on stochastic analysis and related topics, Progress in Probability. (in press). (2001)

[Publications] Shigeki Aida: "On the irreducibility of the Dirichlet forms in infinite dimensional spaces"Osaka J.Math.. (in press). (2001)

[Publications] Shigeki Aida: "Precise Gaussian lower bounds on heat kernels"Stochastics in Finite and Infinite Dimensions. 1-28 (2000)

[Publications] Shigeki Aida: "Stochastic analysis on loop spaces"Sugaku expositions. 13. 197-214 (2000)

[Publications] Shigeki Aida: "Equivalence of heat kernel measure and pinned Wiener measure on loop groups"C.R.Acad.Sci.Paris,. 331. 709-712 (2000)

[Publications] Shigeki Aida: "Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces"J.Funct.Anal.. 174. 430-477 (2000)

[Publications] Keizo Takashima: "Random walk tests and Pseudorandom number generators"Proceedings of International Conference of Mathematical Analysis and Applications, Gyeongsang National Univ.. (in press). (2001)

[Publications] Keizo Takashima: "Hybrid pseudo-random number generation"Monte Carlo Methods and Applications. 6. 49-59 (2000)

[Publications] M.Denker: "Sierpinski gasket as a Martin boundary I"Potential Analysis. (in press). (2001)

[Publications] A.Danilenko: "On measure theoretical analogue of the Takesaki structure theorem for type III factors"Colloquim Mathematicum. 84/85. 485-493 (2000)

[Publications] Toshihiro Hamachi: "On nonsingular Chacon transformations"Illinois Journal Math.. 44. 1-16 (2000)

[Publications] Toshihiro Hamachi: "Canonical subrelations of ergodic equivalence relation-subrelations"Journal of Operator Theory. 43. 3-34 (2000)

久保泉広島大学, 大学院・理学研究科, 教授 (70022621)