1996 年度実績報告書

白色雑音系の確率論および解析的研究

研究課題

研究課題/領域番号	07454033
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	中村宗敬広島大学, 理学部, 助手 (10227944) 大和祐一広島大学, 理学部, 助手 (70112175) 竹中茂夫岡山理科大学, 理学部, 教授 (80022680) 平良和昭広島大学, 理学部, 教授 (90016163) 大春愼之助広島大学, 理学部, 教授 (40063721)
キーワード	White noise / 超汎関数 / ガウス測度 / 非線形方程式 / セミグループ / 拡散過程 / ランダムフラクタル / ナンバー作用素
研究概要	白色雑音系を記述するための基礎空間は、申請者等によって、幾種もの特徴の異なる構成法が与えられたが、必ずしも直接的ではない恨みが残っていた。荷重ナンバー作用素を用いた直接的な構成に成功し、国際会議等で発表した。その結果、二つの異なった〃超確率変数〃の取扱い方の相違点・類似点が明確になった。各分担者は代表者の問題意識に注意を払いながら、それぞれ本来の専門分野での研究に成果をあげた。大春は、非線形的に摂動されたセミグループの特徴付けや局所リプシッツ作用素のセミグループの理論と応用の研究を行った。平良は、積分・偏微分作用素の境界値問題、そのセミグループ、特にフェラ-セミグループの構成の研究を行い、マルコフ過程の研究を行った。竹中は、自己相似な安定過程の構成と特徴付けの研究を深めた。その際に有効なスペクトルの議論が安定過程の白色雑音の研究に重要な役割を果たすと考えられる。中村は、ランダムなフラクタル集合の研究を行い、そのハウスドルフ次元とパッキング次元、ハウスドルフ測度を調べた。当初の目標であった無限次元Bargmann空間とLevyのラプラシアンの研究から、その基礎となる部分に研究の焦点が移行したが、それにより新たな展望が開けてきており、無限次元の偏微分作用素、セミグループ、拡散過程の研究を通じて、白色雑音系の構造がさらに明らかにされる期待が大きくなった。新しい発展としては、H.-H.Kuoとの共同研究の結果、超汎関数空間の新しいクラスを導入し、その特徴付けを一変数の整関数空間の性質を利用して与えることができた。そのクラスが広いことと、一方指数関数をテスト汎関数に持つことから、広い応用が期待される。

研究成果
(29件)

すべてその他

すべて文献書誌 (29件)

[文献書誌] 久保泉: "Non-isotropic Ornstein-Uhlenbeck process and white noise analysis" Proc. of Conference on Stochastic Differential and Differentia Equations. (in pres). (1997)
[文献書誌] 馬場良和、久保泉高橋陽一郎: "Li-Yorke's scrambled sets have measue 0" Nonlinear Analysis, Theory and Methods. 22. 1611-1162 (1996)
[文献書誌] 久保泉: "Weighted number operators and associated processes in white noise analysis" Infinite dimensional harmonic Analysis. 146-155 (1996)
[文献書誌] 久保泉: "Generalized functionals in white noise analysis" Probability Theory and Mathematical Statistics, World $break Scientific. 237-243 (1996)
[文献書誌] 久保泉,H. -H. Kuo: "A simple proof of Hida distribution characterizaiton theorem" Exploring Stochastic Laws. 243-250 (1996)
[文献書誌] 久保泉、横井嘉孝: "Generalized functions and functionals in fluctuation" Mathematical Approach to Fluctuations II, World Scientific. 203-230 (1995)
[文献書誌] 久保泉, H. -H. Kuo: "Finite dimensional Hida distributions" Journal of Functional Analysis. 128. 1-47 (1996)
[文献書誌] 大春槇之助 K. Okamoto: "Nonlinear evolution operaters associated with nonlinear degenerate parabolic cquations" Advances in Mathematical Sciences and Applications. 7 (in press). (1998)
[文献書誌] 大春槇之助 J. A. Goldstein, T. Takahashi: "A class of semigroups of locally Lipshitzian operators and its application to generalized Kortweg-de Vries cquations" Evolution Equations and Nonlinear Problems. (1996)
[文献書誌] 大春槇之助: "Nonlinear perturbations of a class of integrated semigroups" Hiroshima Mathematical. Journal. 26. 433-473 (1996)
[文献書誌] 大春槇之助: "The favard class for a nonlincar parabolic problem" Recent Developement in Evolution Equation. 1-14 (1996)
[文献書誌] 平良和昭,梅津: "Semilinear Elliptic Boundary Value Problems in Chemical Reactor Theory" (in press). (1997)
[文献書誌] 平良和昭: "Boudary value problems, Feller semigroups and Markov processes" Lecture notes in pure and applied mathematics. 175. 421-439 (1996)
[文献書誌] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems" Structure of Solutions of Differential Equations. 425-456 (1996)
[文献書誌] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems III" Advances in Differential Equations. 1. 709-727 (1996)
[文献書誌] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems I" Collectanea Mathematica. 47. 207-229 (1996)
[文献書誌] 平良和昭: "Boundary value problems for elliptic integro-differential operators" Mathematische Zeitschrift. 22. 305-327 (1996)
[文献書誌] 平良和昭: "On boundary value problems of nonlinear elastostatics," Osaka Journal of Mathematics. 33. 553-583 (1996)
[文献書誌] 平良和昭: "The Yamabe problem and nonlinear boundary value problems" Journal of Differential Equations. 122. 316-372 (1995)
[文献書誌] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems II" Tokyo Journal of Mathematics. 19. 387-396 (1996)
[文献書誌] 平良和昭: "Boundary value problems for elliptic pseudo-differential operators" Proc. America Math. Soc.123. 2519-2528 (1995)
[文献書誌] 平良和昭: "On the existence of Feller semigroups with boudary conditions II" J. Func. Anal.129. 108-131 (1995)
[文献書誌] 平良和昭: "An index formula for the de Rham complex" Tohoku Math. J.45. 331-358 (1995)
[文献書誌] 中村宗敬: "On dimensions and measures of statistically constructed Cantor sets" Proc. of The 25th Conference of Stochastic Process and its Applications. (in press). (1997)
[文献書誌] 中村宗敬: "On absolutely continuous invariant measures with respect to Hausdorff measures on self-similar sets" Hiroshima Math. J.26. 1-24 (1996)
[文献書誌] 中村宗敬,中田寿夫: "On the Julia sets of rational functions of degree two with real two parameters" Hiroshima Mathematical Journal. 26. 253-275 (1996)
[文献書誌] 久保泉・矢野公一: "力学系1" 岩波書店(in press), 160 (1997)
[文献書誌] 平良和昭: "Analytic semigroups and semilinear initial boundary value problem" Cambridge University Press, (1995)
[文献書誌] 平良和昭: "London Math. Soc. Lecture Notes Series" Analytic semigroups and semilinear initial boundary value problem, (1995)

1996 年度 実績報告書

白色雑音系の確率論および解析的研究

研究代表者

久保 泉 広島大学, 理学部, 教授 (70022621)

研究成果

[文献書誌] 久保 泉: "Non-isotropic Ornstein-Uhlenbeck process and white noise analysis" Proc. of Conference on Stochastic Differential and Differentia Equations. (in pres). (1997)

[文献書誌] 馬場良和、久保泉 高橋陽一郎: "Li-Yorke's scrambled sets have measue 0" Nonlinear Analysis, Theory and Methods. 22. 1611-1162 (1996)

[文献書誌] 久保 泉: "Weighted number operators and associated processes in white noise analysis" Infinite dimensional harmonic Analysis. 146-155 (1996)

[文献書誌] 久保 泉: "Generalized functionals in white noise analysis" Probability Theory and Mathematical Statistics, World $break Scientific. 237-243 (1996)

[文献書誌] 久保泉,H. -H. Kuo: "A simple proof of Hida distribution characterizaiton theorem" Exploring Stochastic Laws. 243-250 (1996)

[文献書誌] 久保泉、横井嘉孝: "Generalized functions and functionals in fluctuation" Mathematical Approach to Fluctuations II, World Scientific. 203-230 (1995)

[文献書誌] 久保泉, H. -H. Kuo: "Finite dimensional Hida distributions" Journal of Functional Analysis. 128. 1-47 (1996)

[文献書誌] 大春槇之助 K. Okamoto: "Nonlinear evolution operaters associated with nonlinear degenerate parabolic cquations" Advances in Mathematical Sciences and Applications. 7 (in press). (1998)

[文献書誌] 大春槇之助 J. A. Goldstein, T. Takahashi: "A class of semigroups of locally Lipshitzian operators and its application to generalized Kortweg-de Vries cquations" Evolution Equations and Nonlinear Problems. (1996)

[文献書誌] 大春槇之助: "Nonlinear perturbations of a class of integrated semigroups" Hiroshima Mathematical. Journal. 26. 433-473 (1996)

[文献書誌] 大春槇之助: "The favard class for a nonlincar parabolic problem" Recent Developement in Evolution Equation. 1-14 (1996)

[文献書誌] 平良和昭,梅津: "Semilinear Elliptic Boundary Value Problems in Chemical Reactor Theory" (in press). (1997)

[文献書誌] 平良和昭: "Boudary value problems, Feller semigroups and Markov processes" Lecture notes in pure and applied mathematics. 175. 421-439 (1996)

[文献書誌] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems" Structure of Solutions of Differential Equations. 425-456 (1996)

[文献書誌] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems III" Advances in Differential Equations. 1. 709-727 (1996)

[文献書誌] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems I" Collectanea Mathematica. 47. 207-229 (1996)

[文献書誌] 平良和昭: "Boundary value problems for elliptic integro-differential operators" Mathematische Zeitschrift. 22. 305-327 (1996)

[文献書誌] 平良和昭: "On boundary value problems of nonlinear elastostatics," Osaka Journal of Mathematics. 33. 553-583 (1996)

[文献書誌] 平良和昭: "The Yamabe problem and nonlinear boundary value problems" Journal of Differential Equations. 122. 316-372 (1995)

[文献書誌] 平良和昭: "Bifurcation for nonlinear elliptic boundary value problems II" Tokyo Journal of Mathematics. 19. 387-396 (1996)

[文献書誌] 平良和昭: "Boundary value problems for elliptic pseudo-differential operators" Proc. America Math. Soc.123. 2519-2528 (1995)

[文献書誌] 平良和昭: "On the existence of Feller semigroups with boudary conditions II" J. Func. Anal.129. 108-131 (1995)

[文献書誌] 平良和昭: "An index formula for the de Rham complex" Tohoku Math. J.45. 331-358 (1995)

[文献書誌] 中村宗敬: "On dimensions and measures of statistically constructed Cantor sets" Proc. of The 25th Conference of Stochastic Process and its Applications. (in press). (1997)

[文献書誌] 中村宗敬: "On absolutely continuous invariant measures with respect to Hausdorff measures on self-similar sets" Hiroshima Math. J.26. 1-24 (1996)

[文献書誌] 中村宗敬,中田寿夫: "On the Julia sets of rational functions of degree two with real two parameters" Hiroshima Mathematical Journal. 26. 253-275 (1996)

[文献書誌] 久保泉・矢野公一: "力学系1" 岩波書店(in press), 160 (1997)

[文献書誌] 平良和昭: "Analytic semigroups and semilinear initial boundary value problem" Cambridge University Press, (1995)

[文献書誌] 平良和昭: "London Math. Soc. Lecture Notes Series" Analytic semigroups and semilinear initial boundary value problem, (1995)

1996 年度実績報告書

久保泉広島大学, 理学部, 教授 (70022621)

[文献書誌] 久保泉: "Non-isotropic Ornstein-Uhlenbeck process and white noise analysis" Proc. of Conference on Stochastic Differential and Differentia Equations. (in pres). (1997)

[文献書誌] 馬場良和、久保泉高橋陽一郎: "Li-Yorke's scrambled sets have measue 0" Nonlinear Analysis, Theory and Methods. 22. 1611-1162 (1996)

[文献書誌] 久保泉: "Weighted number operators and associated processes in white noise analysis" Infinite dimensional harmonic Analysis. 146-155 (1996)

[文献書誌] 久保泉: "Generalized functionals in white noise analysis" Probability Theory and Mathematical Statistics, World $break Scientific. 237-243 (1996)