平衡確率現象の総合的研究

1998 年度 実績報告書

• 研究課題/領域番号: 10304006
• 研究種目: 基盤研究(A)
• 研究機関: 広島大学
• 研究代表者: 久保 泉 広島大学, 理学部, 教授 (70022621)
• 研究分担者: 前島 信 慶応大学, 理工学部, 教授 (90051846) ; 井原 俊輔 名古屋大学, 情報文化学部, 教授 (00023200) ; 舟木 直久 東京大学大学院, 数理科学研究科, 教授 (60112174) ; 平良 和昭 筑波大学, 数学系, 教授 (90016163) ; 岩田 耕一郎 広島大学, 理学部, 助教授 (20241292)
• キーワード: 確率論 / 平衡現象 / 複雑系 / フラクタル / ガウス過程 / 安定過程 / 情報理論

研究概要

本研究課題で、以下のようなテーマで研究集会を開催した:「生物現象と非線形微分方程式」「複雑系現象と実証分析」「ガウス過程と量子解析」「Fractal and Analysis」「エルゴード理論、情報理論とその周辺」「安定過程及びその応用」「安定過程及びその応用」「確率論における諸問題」。また仏国より、Kahane教授を招き、古典的な解析学の伝統にも目を配った先端的な確率論の研究の観点から、レビューを受けた。
これらの研究集会で活発に行われた討論を通して、生物現象、複雑系、量子物理学、情報理論における平衡確率現象の研究の深化と今後の重要課題が明確になって来た。また、安定過程、エルゴード理論・フラクタルなど、本来的に平衡状態あるいは極限状態における現象を確率論的現象と見て捉える研究が平衡確率現象と言う視点からより幅広い研究に位置づけられた。

研究成果

• [文献書誌] 久保泉: "Entire functionals and generalized functionals in white noise analysis" Analysis on infinite-dimensional Lie groups and algebra. 207-215 (1998)
• [文献書誌] 久保泉: "White noise analysis associated with sequences of numbers"" Infinite Dimensional Analysis Quantum Probability and Related Topics. (in press). (1998)
• [文献書誌] 岩田耕一郎: "Markov Property and cokernels of Local Operators." London Math.Soc. (2). 56. 657-672 (1998)
• [文献書誌] 平良和昭: "Feller semigroups with boundary conditions," Proceedings of the third international conference on Functional Analysis and Approximation Theory. 52. 157-173 (1998)
• [文献書誌] 平良和昭: "Semilinear elliptic boundary value problems in chemical reactor theory" Journal of Differential Equations. 142. 434-454 (1998)
• [文献書誌] 平良和昭: "Introduction to semilinear elliptic boundary value problems" Taiwanese Journal of Mathematics. 2. 127-172 (1998)
• [文献書誌] 平良和昭: "Boundary value problems of nonlinear elastostatics" Proceedings of the Conference on Generalized Analytic Functions-Theory and Applications. 183-195 (1998)
• [文献書誌] 平良和昭: "Bifurcation theory for semilinear elliptic boundary value problems" Hiroshima Mathematical Journal. 28. 261-308 (1998)
• [文献書誌] 平良和昭: "A degenerate Neumann problem for quasilinear elliptic integro-differential operators" Mathematische Zeitschrift. (in press). (1999)
• [文献書誌] 平良和昭: "Positive solutions of semilinear elliptic boundary value problems in chemical reactor theory" Proceedings of the International Society for Analysis,Applications and Computation '97 Congress. (in press). (1999)
• [文献書誌] 平良和昭: "Feller Semigroups and degenerate elliptic operators I" Conferenze del Seminario di Matematica dell'Universit {a} di Bari. 275 (in press). (1999)
• [文献書誌] 平良和昭: "A degenerate Neumann problem for quasilinear elliptic equations" Tokyo Journal of Mathematics. 23. (2000)
• [文献書誌] 平良和昭: "Brownian motion,de Rham complex and index formulas" Proceedings of SAP'98 : Trends in Probability and Related Analysis. (in press). (1999)
• [文献書誌] 平良和昭: "Stability in chemical reactor theory" proceedings of the Sixth International Conference on Evolution Equations and their Applications in Physical and Life Sciences. (in press). (1999)
• [文献書誌] 井原俊輔: "Information transmission over continuous-time Gaussian channels with feedback" Problems of Information Transmission. (in press). (1999)
• [文献書誌] 井原俊輔: "Large deviation theorems for Gaussian processes and their applications in information theory"
• [文献書誌] P.Biler: "Fractal Burgers equations" J.Differential Equations. 148 (in press). (1998)
• [文献書誌] 舟木直久: "相分離の確率モデルと界面の運動方程式" 数学. 50. 68-85
• [文献書誌] 舟木直久: "Interacting particle approximation for fractal Burgers equation" Stochastic Processes and Related Topics,. 141-166 (1998)
• [文献書誌] 舟木直久: "Free boundary problem from stochastic lattice gas model" Annals Institut Henri Poincare. (in press). (1999)
• [文献書誌] 舟木直久: "Recent results on the Ginzburg-Landau \$nabla $phi\ interface model" Proceedings of the Workshop on "Hydrodynamic Limits",Fields Institute Communications and Monograph Series. (in press). (1999)
• [文献書誌] 舟木直久: "Singular limit for stochastic reaction-diffusion equation and generation of random interfaces" Acta Mathematica Sinica,Series (B). (in press). (1999)
• [文献書誌] D.M.Chung: "Transformations on white noise functions associated with second order differential operators of diagonal type" Nagoya Math.J.173-192 (1998)
• [文献書誌] L.Accardi: "Notions of independence related to the free group" Infinite Dim.Anal.Quantum Prob.1. 201-220
• [文献書誌] 尾畑伸明: "A note on Hida's whiskers and complex white noise" Analysis on Infinite-Dimensional Lie Groups and Algebras. 321-336 (1998)
• [文献書誌] D.M.Chung: "Higher powers of quantum white noises in terms of integral kernel operators" nfinite Dim.Anal.Quantum Prob.1. 553-559 (1998)
• [文献書誌] 尾畑伸明: "Wick product of white noise operators and quantum stochastic differential equations" J.Math.Soc.Japan. 51 (in press). (1999)
• [文献書誌] 尾畑伸明: "Normal-ordered white noise differential equations II : Regularity properties of solutions" Proc.7th Vilnius Conference,1998. (in press). (1999)
• [文献書誌] 高嶋恵三: "Random walk tests of pseudorandom number generations by cellular automata" Proceedings of the 3-rd St.Peterburg Workshop on Simulation. 302-305 (1998)
• [文献書誌] 高嶋恵三: "Random walk tests and Pseudorandom number generators" Proceedings of International Conference of Mathematical Analysis and Applications. (in press). (1999)
• [文献書誌] 会田茂樹: "ループ空間上の確率解析" 数学. 50. 265-281 (1998)
• [文献書誌] 会田茂樹: "Uniform Positivity Improving Property,Sobolev Inequalitiesand Spectral Gaps" Journal of Functional Analysis. 158. 152-185 (1998)
• [文献書誌] 会田茂樹: "Differential Calculus on Path and Loop Spaces,II Irreducibility of Dirichlet Forms on Loop Spaces" Bull.Sci.Math.122. 635-666 (1998)
• [文献書誌] 前島信: "Norming operators for operator-self-similar processes.Stochastic processes and related topics" Trends Math.,Birkhauser Boston. 287-295 (1998)
• [文献書誌] 前島信: "Moments of limits of lightly trimmed sums of random vectors in the generalized domain of normal attraction of non-Gaussian operator-stable laws" Ann.Inst.Statist.Math.49. 737-747 (1998)
• [文献書誌] 平良和昭: "Brownian motion and index formulas for the de Rham complex" Mathematical Research,No$.106,WILEY-VCH, 230 (1998)