1999 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, 理学部, 教授 (70022621)
Co-Investigator(Kenkyū-buntansha)	前島信慶応大学, 理工学部, 教授 (90051846) 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) 佐藤坦九州大学, 大学院・数理学研究科, 教授 (30037254) 井原俊輔名古屋大学, 情報文化学部, 教授 (00023200)
Keywords	確率論 / 平衡現象 / 複雑系 / フラクタル / エルゴード理論 / 情報理論 / 確率解析
Research Abstract	昨年度に引き続き、平衡状態における確率現象および、平衡状態への移行の機構を明らかにすることを目的とした研究を行った。今年度は、次のようなシンポジュウムやワークショップを開催して、研究の方向の確認を行うと共に、研究成果の発表を行った。「力学系とフラクタル」,「Symbolic Dynamics and Its Related Fields」, 「無限次元調和解析」,「確率解析とその周辺」, 「量子確立解析とその周辺」, 「情報解析に関する理論的あるいは実証的研究」,「エルゴード理論の展望」, 「生物現象と非線形微分方程式」,「フラクタルの調和解析と複素力学系」, 「量子計算と確率現象ワークショップ」特に、「力学系とフラクタル」のワークショップには、力学系およびマルチフラクタルの権威者であるYakov B.Pesin 教授を招聘し、本課題研究のレヴューを受けた。また、C.Lecot 教授を招聘して、確率解析における数値計算に関する共同研究を行うとともに、本課題における数値確率解析や乱数理論の研究に関するレヴューを受けた。これらの研究活動により、複雑系・カオス・フラクタル・エルゴード理論、量子確率解析・量子計算・生物現象などの研究を平衡確率現象の立ち場から深化させることができた。

Research Products
(42 results)

All Other

All Publications (42 results)

[Publications] Izumi Kubo et al.: "White noise analysis associated with sequences of numbers"Infinite Dimensional Analysis,Quantum Probability and Related Topics. 2. 315-336 (1999)
[Publications] Izumi Kubo et al.: "Bell numbers,Log-concavity"Recent developments in Stochastic Analysis. (in press). (2000)
[Publications] Izumi Kubo et al.: "Characterization of Hida Measures in white noise"Proc.for Japan-Germany Conference 99 at Kyoto Univ. (in press). (2000)
[Publications] Izumi Kubo et al.: "CKS-space in terms of growth functions"Proc.of Second International Conference on Quantum Information. (in press). (2000)
[Publications] Izumi Kubo et al.: "Characterization of test functions in CKS-space"Proceedings of International Conference on Mathmetical Physics and Stochastic Processes. (in press). (2000)
[Publications] Kazuaki Taira et al.: "A degenerate Neumann problem for quasilinear elliptic integro-differential operators"Mathematische Zeitschrift. 230. 679-694 (1999)
[Publications] Makoto Maejima et al.: "Some multivariate infinitely divisible distributions and their projections"Probab.Math.Statist.. (in press). (2000)
[Publications] Nobuaki Obata: "A note on normal-ordered white noise equations,"Invited Lectures at the VIII-th Internat.Colloq.Differential Equations Vol.II. 109-118 (1999)
[Publications] Nobuaki Obata et al.: "Wick product of white noise operators and quantum stochastic differential equations"J.Math.Soc.Japan. 51. 613-641 (1999)
[Publications] Nobuaki Obata et al.: "A method for information analysis of sequences by two-dimensional pattern formation with coloration,"Quantum Information. 27-58 (1999)
[Publications] Nobuaki Obata et al.: "Normal-ordered white noise differential equations II: Regularity properties of solutions,"Probability Theory and Mathematical Statistics. (in press). (2000)
[Publications] Nobuaki Obata et al.: "White noise operator theory: Fundamental concepts and developing applications"Proceedings of Volterra International School. (in press). (2000)
[Publications] Makoto Maejima et al.: "Semi-selfsimilar processes"J.Theor.Probab.. 12. 347-383 (1999)
[Publications] Makoto Maejima et al.: "Certain probabilistics aspects on semistable laws"Ann.Inst.Statist.Math.. 51. 449-462 (1999)
[Publications] Makoto Maejima et al.: "Operator semi-selfdeconposability,(C,Q)-decomposability and related nested classes,"Tokyo J.Math.. 22. 473-509 (1999)
[Publications] Makoto Maejima et al.: "Completely operator semi-selfdecomposable distribuitons"Tokyo J.Math.. (in press). (2000)
[Publications] Makoto Maejima et al.: "Exponents of semi-selfsimilar processes,"Yokohama Math.J. 47. 93-102 (1999)
[Publications] Makoto Maejima et al.: "Distributions of selfsimilar and semi-selfsimilar processes with independent increments"Statist.Probab.Lett.. (in press). (2000)
[Publications] Shunsuke Ihara: "Information transmission over continuous-time Gaussian channels with feedback."Problems of Information Transmission. 35. 10-24 (1999)
[Publications] Shunsuke Ihara: "Large deviation theorems for Gaussian processes and their applications in information theory"Preprint Series in Math.Sci.,Nagoya Univ.. 1999-2. 1-30 (1999)
[Publications] Tadahisa Funaki: "Free boundary problem from stochastic lattice gas model."Ann.Inst.Henri Poincare. 35. 573-603 (1999)
[Publications] Tadahisa Funaki: "Singular limit for stochastic reaction-diffusion equation and generation of random interfaces."Acta Mathematica Sinica,English Series. 15. 407-438 (1999)
[Publications] Tadahisa Funaki et al.: "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). (2000)
[Publications] Tadahisa Funaki et al.: "Interacting jump Markov processes associated with nonlocal quadratic evolution problems"Probability and Mathematical Statistics. (in press). (2000)
[Publications] Kazuaki Taira: "Feller Semigroups and degenerate elliptic operators I"Conferenze del Seminario di Matematica dell'Universita di Bari. 275. 1-80 (1999)
[Publications] Kazuaki Taira: "Feller Semigroups and degenerate elliptic operators II"Conferenze del Seminario di Matematica dell'Universita di Bari. 276. 1-60 (1999)
[Publications] Kazuaki Taira et al.: "Growing-up positive solutionsof semilinear elliptic boundary value problems"Journal of Mathematical Analysis and Applications. 238. 196-215 (1999)
[Publications] Kazuaki Taira: "Brownian motion,de Rham complex and index formulas,"Trends in Probability and Related Analysis. 159-176 (1999)
[Publications] Kazuaki Taira et al.: "Feller semigroups generated by degenerate elliptic operators,Semigroup"Semigroup Forum. 60. 1-14 (2000)
[Publications] Kazuaki Taira et al.: "A degenerate Neumann problem for quasilinear elliptic equations"Tokyo Journal of Mathematics. 23(in press). (2000)
[Publications] Keizo Takashima et al.: "On a Fractal Approach to Actual Plant Images,"Proceedings of Fifth International Conference on Pattern Recognition and Information Processing. 2. 134-138 (1999)
[Publications] Hiroshi Sato et al.: "Absolute continuity of a symmetric three-valued random translation of a Gaussian sequence."Trends in Probability and Related Analysis. 263-372 (1999)
[Publications] Hiroshi Sato et al.: "Sierpinski gaskes as a Martin boundary I(The Martin Kernels):"Potential Analysis. (in press). (2000)
[Publications] Hiroshi Sato et al.: "Sierpinski gaskes as a Martin boundary II(The Intrinsic Metric):"Publ.RIMS,Kyoto Univ.. (in press). (2000)
[Publications] Toshihiro Hamachi: "Suborbits and group extensions of flows"Israel J.Math. 379-380 (1999)
[Publications] Yasunori Okabe: "On the theory of KM 2O-Langevin equations for stationary flows.I.Characterization theorem"J.Math.Soc.Japan. 51. 817-841 (1999)
[Publications] Nobuaki Obata: "A note on symbols of Fock space operators,"Quantum Information. (in press). (2000)
[Publications] Shigeki Aida: "On the irreducibility of Dirichlet forms on domains in infinite dimensional spaces"Osaka Journal of Mathematics. (in press). (2000)
[Publications] Shigeki Aida: "Logarithmic derivatives of hear kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients"Journal of Functional Analysis. (in press). (2000)
[Publications] Shigeki Aida: "Short time asymptotics of certain infinite dimensional diffusion process,"Proceedings of 7th Workshop of Stochastic anslysis and related topics. (in press). (2000)
[Publications] Shigeki Aida: "On determinism of set-indexed S α S-processes:in"Trends in probability and related analysis 1999. 285-290 (1999)
[Publications] Keizo Tadashima: "Random walk tests and Feedback Polynomials of m-sequences,"Proceedings of Fifth International Conference on Pattern Recognition and Information Processing. 1. 267-271 (1999)

1999 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, 理学部, 教授 (70022621)

Research Products

[Publications] Izumi Kubo et al.: "White noise analysis associated with sequences of numbers"Infinite Dimensional Analysis,Quantum Probability and Related Topics. 2. 315-336 (1999)

[Publications] Izumi Kubo et al.: "Bell numbers,Log-concavity"Recent developments in Stochastic Analysis. (in press). (2000)

[Publications] Izumi Kubo et al.: "Characterization of Hida Measures in white noise"Proc.for Japan-Germany Conference 99 at Kyoto Univ. (in press). (2000)

[Publications] Izumi Kubo et al.: "CKS-space in terms of growth functions"Proc.of Second International Conference on Quantum Information. (in press). (2000)

[Publications] Izumi Kubo et al.: "Characterization of test functions in CKS-space"Proceedings of International Conference on Mathmetical Physics and Stochastic Processes. (in press). (2000)

[Publications] Kazuaki Taira et al.: "A degenerate Neumann problem for quasilinear elliptic integro-differential operators"Mathematische Zeitschrift. 230. 679-694 (1999)

[Publications] Makoto Maejima et al.: "Some multivariate infinitely divisible distributions and their projections"Probab.Math.Statist.. (in press). (2000)

[Publications] Nobuaki Obata: "A note on normal-ordered white noise equations,"Invited Lectures at the VIII-th Internat.Colloq.Differential Equations Vol.II. 109-118 (1999)

[Publications] Nobuaki Obata et al.: "Wick product of white noise operators and quantum stochastic differential equations"J.Math.Soc.Japan. 51. 613-641 (1999)

[Publications] Nobuaki Obata et al.: "A method for information analysis of sequences by two-dimensional pattern formation with coloration,"Quantum Information. 27-58 (1999)

[Publications] Nobuaki Obata et al.: "Normal-ordered white noise differential equations II: Regularity properties of solutions,"Probability Theory and Mathematical Statistics. (in press). (2000)

[Publications] Nobuaki Obata et al.: "White noise operator theory: Fundamental concepts and developing applications"Proceedings of Volterra International School. (in press). (2000)

[Publications] Makoto Maejima et al.: "Semi-selfsimilar processes"J.Theor.Probab.. 12. 347-383 (1999)

[Publications] Makoto Maejima et al.: "Certain probabilistics aspects on semistable laws"Ann.Inst.Statist.Math.. 51. 449-462 (1999)

[Publications] Makoto Maejima et al.: "Operator semi-selfdeconposability,(C,Q)-decomposability and related nested classes,"Tokyo J.Math.. 22. 473-509 (1999)

[Publications] Makoto Maejima et al.: "Completely operator semi-selfdecomposable distribuitons"Tokyo J.Math.. (in press). (2000)

[Publications] Makoto Maejima et al.: "Exponents of semi-selfsimilar processes,"Yokohama Math.J. 47. 93-102 (1999)

[Publications] Makoto Maejima et al.: "Distributions of selfsimilar and semi-selfsimilar processes with independent increments"Statist.Probab.Lett.. (in press). (2000)

[Publications] Shunsuke Ihara: "Information transmission over continuous-time Gaussian channels with feedback."Problems of Information Transmission. 35. 10-24 (1999)

[Publications] Shunsuke Ihara: "Large deviation theorems for Gaussian processes and their applications in information theory"Preprint Series in Math.Sci.,Nagoya Univ.. 1999-2. 1-30 (1999)

[Publications] Tadahisa Funaki: "Free boundary problem from stochastic lattice gas model."Ann.Inst.Henri Poincare. 35. 573-603 (1999)

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

[Publications] Tadahisa Funaki et al.: "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). (2000)

[Publications] Tadahisa Funaki et al.: "Interacting jump Markov processes associated with nonlocal quadratic evolution problems"Probability and Mathematical Statistics. (in press). (2000)

[Publications] Kazuaki Taira: "Feller Semigroups and degenerate elliptic operators I"Conferenze del Seminario di Matematica dell'Universita di Bari. 275. 1-80 (1999)

[Publications] Kazuaki Taira: "Feller Semigroups and degenerate elliptic operators II"Conferenze del Seminario di Matematica dell'Universita di Bari. 276. 1-60 (1999)

[Publications] Kazuaki Taira et al.: "Growing-up positive solutionsof semilinear elliptic boundary value problems"Journal of Mathematical Analysis and Applications. 238. 196-215 (1999)

[Publications] Kazuaki Taira: "Brownian motion,de Rham complex and index formulas,"Trends in Probability and Related Analysis. 159-176 (1999)

[Publications] Kazuaki Taira et al.: "Feller semigroups generated by degenerate elliptic operators,Semigroup"Semigroup Forum. 60. 1-14 (2000)

[Publications] Kazuaki Taira et al.: "A degenerate Neumann problem for quasilinear elliptic equations"Tokyo Journal of Mathematics. 23(in press). (2000)

[Publications] Keizo Takashima et al.: "On a Fractal Approach to Actual Plant Images,"Proceedings of Fifth International Conference on Pattern Recognition and Information Processing. 2. 134-138 (1999)

[Publications] Hiroshi Sato et al.: "Absolute continuity of a symmetric three-valued random translation of a Gaussian sequence."Trends in Probability and Related Analysis. 263-372 (1999)

[Publications] Hiroshi Sato et al.: "Sierpinski gaskes as a Martin boundary I(The Martin Kernels):"Potential Analysis. (in press). (2000)

[Publications] Hiroshi Sato et al.: "Sierpinski gaskes as a Martin boundary II(The Intrinsic Metric):"Publ.RIMS,Kyoto Univ.. (in press). (2000)

[Publications] Toshihiro Hamachi: "Suborbits and group extensions of flows"Israel J.Math. 379-380 (1999)

[Publications] Yasunori Okabe: "On the theory of KM 2O-Langevin equations for stationary flows.I.Characterization theorem"J.Math.Soc.Japan. 51. 817-841 (1999)

[Publications] Nobuaki Obata: "A note on symbols of Fock space operators,"Quantum Information. (in press). (2000)

[Publications] Shigeki Aida: "On the irreducibility of Dirichlet forms on domains in infinite dimensional spaces"Osaka Journal of Mathematics. (in press). (2000)

[Publications] Shigeki Aida: "Logarithmic derivatives of hear kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients"Journal of Functional Analysis. (in press). (2000)

[Publications] Shigeki Aida: "Short time asymptotics of certain infinite dimensional diffusion process,"Proceedings of 7th Workshop of Stochastic anslysis and related topics. (in press). (2000)

[Publications] Shigeki Aida: "On determinism of set-indexed S α S-processes:in"Trends in probability and related analysis 1999. 285-290 (1999)

[Publications] Keizo Tadashima: "Random walk tests and Feedback Polynomials of m-sequences,"Proceedings of Fifth International Conference on Pattern Recognition and Information Processing. 1. 267-271 (1999)

久保泉広島大学, 理学部, 教授 (70022621)