1993 Fiscal Year Annual Research Report

確率論および関連した解析学の諸問題の研究

Research Project

Project/Area Number	04452011
Research Institution	Keio University
Principal Investigator	田中洋慶應義塾大学, 理工学部, 教授 (70011468)
Co-Investigator(Kenkyū-buntansha)	田村要造慶應義塾大学, 理工学部, 講師 (50171905) 前田吉昭慶應義塾大学, 理工学部, 助教授 (40101076) 菊地紀夫慶應義塾大学, 理工学部, 教授 (80090041) 伊藤雄二慶應義塾大学, 理工学部, 教授 (90112987) 前島信慶應義塾大学, 理工学部, 教授 (90051846)
Keywords	拡散過程 / ブラウン運動 / ランダム媒質 / オヘレーター安定過程 / II∞、III型のエルゴード的変換 / 調和写像とモース・フロー / 無限次元Lie環 / ポアンカレ・バーコフ・ウイットの定理
Research Abstract	本研究は、確率論、エルゴード論、微分方程式、微分幾何等の研究者により、確率論および(周辺)解析学について研究を行ったものである。その成果は研究発表の欄にあるように多くの雑誌に発表されている。 1.ランダム媒質の確率論については田中が以前より研究して来た。今年度の主な成果はウイナー媒質の中のブラウン運動の局在性の問題に対し従来のものより精密な形での解答を与えた。またドリフトをもつウイナー媒質の中のブラウン運動の極限的挙動についての新しい結果を得た。自己相似系の確率論的研究のひとつとして自己相似過程の研究が行われた。とくに前島はオペレーター安定過程の基本的性質、例、その極限定理との関係について新しい結果を得た。 2.エルゴード理論の研究において、伊藤は有限不変測度をもたないエルゴード的変換に特有な性質を種々の観点から調べ、とくに付随するコサイクルの性質を通して変換の分類問題に対する新しい知見を得た。 3.非線型偏微分方程式の研究においては、菊地により調和写像型の滑らかなモース・フローの構成がなされた。それはある変分汎関数列を考えるもので、その汎関係列に対応するオイラー・ラグランジュ方程式の解析に基づいている。 4.前田は、無限次元ILH-Lie環に自然に定められるポアソン構造について、その代数的構造の変形可能性を証明した。これは有限次元Lie環に対するポアンカレ・バーコフ・ウイットの定理の無限次元への拡張である。

Research Products
(24 results)

All Other

All Publications (24 results)

[Publications] H.Tanaka: "Recurrence of a diffusion process in a multidimensional Brownian environment" Proceedings of the Japan Academy. 69 Ser.A. 377-381 (1993)
[Publications] H.Tanaka: "Localization of a diffusion process in a one-dimensional Brownian environment" Communications on Pure and Applied Mathematics. (発表予定). (1994)
[Publications] K.Kawazu: "On the maximum of a diffusion process in a drifted Brownian environment" Lecture Notes in Mathematics (Seminaire de Probabilites XXVII.Springer-Verlag). 1557. 78-85 (1993)
[Publications] M.Maejima: "Trimmed sums of i.i.d.Banach space valued random variables" Journal of Theoretical Probability. 6. 57-69 (1993)
[Publications] M.Maejima: "Operator-self-similar stable processes" Stochastic Processes and Their Applications. (発表予定). (1994)
[Publications] M.Maejima: "Operator-stable processes and operator fractional stable motions" Probability and Mathematical Statistics. (発表予定). (1994)
[Publications] N.Kikuchi: "Holder estimates of solutions for difference-differential equations of elliptic-parabolic type" Journal of Geometric Analysis. (発表予定). (1994)
[Publications] N.Kikuchi: "A method of constructing Morse flows to variational functional" Nonlinear World. (発表予定). (1994)
[Publications] N.Kikuchi: "On the higher integrability of the gradients of the solutions to difference partial differential systems of elliptic-parabolic type" Mathematische Zeitschrift. (発表予定). (1994)
[Publications] H.Omori: "Non-commutative complex projective space" Advanced Studies in Pure Mathematics. 22. 133-152 (1993)
[Publications] H.Omori: "The uniqueness of star products on P_n(C)" differential Geometry Proceedings of the Symposium in honour of Professor Su Buchin. 170-176 (1993)
[Publications] Y.Maeda: "The mean curvature of Gauge orbits" Global Analysis in Modern Mathematics(Symposium in honor of R.Palai´s sixties birthday). 171-220 (1993)
[Publications] H.Omori: "A Poincare-Birkhoff-Witt theorem for infinite dimensional Lie algebeas" Journal of Mathematical Society of Japan. 46. 25-50 (1994)
[Publications] V.A.Solonnikov: "Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid,The Navier-Stokes equations II" Theory and Numerical Methods(Lecture Notes in Mathematics,Springer-Verlag). 1530. 30-55 (1994)
[Publications] V.A.Solonnikov: "Equilibrium figures of slowly rotating viscous compressible barotropic capillary liquid" Advances in Mathematical Science and Applications. 2. 139-145 (1993)
[Publications] T.Nishiyama: "Solvability of the localized induction equation for vortex motion" Communications in Mathematical Physics. (発表予定). (1994-5)
[Publications] N.Tanaka: "Large-time existence of surface waves of compressible viscous fluid" Proceedings of the Japan Academy. 67,Ser.A. 230-233 (1993)
[Publications] K.Komatsu: "On unramified Galois extensions of certain algebraic number fields" Tokyo Journal of Mathematics. 16. 351-354 (1993)
[Publications] I.Ishii: "Fake braid group and 3-manifolds" Geomery and its Applications (edited by T.Nagano et al.,World Scientific). 51-58 (1993)
[Publications] S.Shimomura: "Asymptotic expansions and Stokes multipliers of the confluent hypergeometric function PHI_2,I" Proceedings of Royal Society of Edinburgh. 123A. 1165-1177 (1993)
[Publications] Y.Yamaura: "A free boundary problem for minimal surface equation" Bollettino Della Unione Matematica Italiana. (発表予定). (1994-5)
[Publications] Y.Yamaura: "A uniform estimate of the perimeter for minimizers of a free boundary problem" Rendiconti di Matematica e Delle Sue Applicazioni. (発表予定). (1994-5)
[Publications] Y.Yamaura: "The regularity of minimizers of a radially symmetric free boundary problem" Annali dell Universita di Ferrara. (発表予定). (1994-5)
[Publications] H.Sano: "Modified Gronwall s inequality and its application to stabilization problem for semilinear parabolic systems" Systems and Control Letters. (21Issue 3). (1993)

1993 Fiscal Year Annual Research Report

確率論および関連した解析学の諸問題の研究

Principal Investigator

田中 洋 慶應義塾大学, 理工学部, 教授 (70011468)

Research Products

[Publications] H.Tanaka: "Recurrence of a diffusion process in a multidimensional Brownian environment" Proceedings of the Japan Academy. 69 Ser.A. 377-381 (1993)

[Publications] H.Tanaka: "Localization of a diffusion process in a one-dimensional Brownian environment" Communications on Pure and Applied Mathematics. (発表予定). (1994)

[Publications] K.Kawazu: "On the maximum of a diffusion process in a drifted Brownian environment" Lecture Notes in Mathematics (Seminaire de Probabilites XXVII.Springer-Verlag). 1557. 78-85 (1993)

[Publications] M.Maejima: "Trimmed sums of i.i.d.Banach space valued random variables" Journal of Theoretical Probability. 6. 57-69 (1993)

[Publications] M.Maejima: "Operator-self-similar stable processes" Stochastic Processes and Their Applications. (発表予定). (1994)

[Publications] M.Maejima: "Operator-stable processes and operator fractional stable motions" Probability and Mathematical Statistics. (発表予定). (1994)

[Publications] N.Kikuchi: "Holder estimates of solutions for difference-differential equations of elliptic-parabolic type" Journal of Geometric Analysis. (発表予定). (1994)

[Publications] N.Kikuchi: "A method of constructing Morse flows to variational functional" Nonlinear World. (発表予定). (1994)

[Publications] N.Kikuchi: "On the higher integrability of the gradients of the solutions to difference partial differential systems of elliptic-parabolic type" Mathematische Zeitschrift. (発表予定). (1994)

[Publications] H.Omori: "Non-commutative complex projective space" Advanced Studies in Pure Mathematics. 22. 133-152 (1993)

[Publications] H.Omori: "The uniqueness of star products on P_n(C)" differential Geometry Proceedings of the Symposium in honour of Professor Su Buchin. 170-176 (1993)

[Publications] Y.Maeda: "The mean curvature of Gauge orbits" Global Analysis in Modern Mathematics(Symposium in honor of R.Palai´s sixties birthday). 171-220 (1993)

[Publications] H.Omori: "A Poincare-Birkhoff-Witt theorem for infinite dimensional Lie algebeas" Journal of Mathematical Society of Japan. 46. 25-50 (1994)

[Publications] V.A.Solonnikov: "Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid,The Navier-Stokes equations II" Theory and Numerical Methods(Lecture Notes in Mathematics,Springer-Verlag). 1530. 30-55 (1994)

[Publications] V.A.Solonnikov: "Equilibrium figures of slowly rotating viscous compressible barotropic capillary liquid" Advances in Mathematical Science and Applications. 2. 139-145 (1993)

[Publications] T.Nishiyama: "Solvability of the localized induction equation for vortex motion" Communications in Mathematical Physics. (発表予定). (1994-5)

[Publications] N.Tanaka: "Large-time existence of surface waves of compressible viscous fluid" Proceedings of the Japan Academy. 67,Ser.A. 230-233 (1993)

[Publications] K.Komatsu: "On unramified Galois extensions of certain algebraic number fields" Tokyo Journal of Mathematics. 16. 351-354 (1993)

[Publications] I.Ishii: "Fake braid group and 3-manifolds" Geomery and its Applications (edited by T.Nagano et al.,World Scientific). 51-58 (1993)

[Publications] S.Shimomura: "Asymptotic expansions and Stokes multipliers of the confluent hypergeometric function PHI_2,I" Proceedings of Royal Society of Edinburgh. 123A. 1165-1177 (1993)

[Publications] Y.Yamaura: "A free boundary problem for minimal surface equation" Bollettino Della Unione Matematica Italiana. (発表予定). (1994-5)

[Publications] Y.Yamaura: "A uniform estimate of the perimeter for minimizers of a free boundary problem" Rendiconti di Matematica e Delle Sue Applicazioni. (発表予定). (1994-5)

[Publications] Y.Yamaura: "The regularity of minimizers of a radially symmetric free boundary problem" Annali dell Universita di Ferrara. (発表予定). (1994-5)

[Publications] H.Sano: "Modified Gronwall s inequality and its application to stabilization problem for semilinear parabolic systems" Systems and Control Letters. (21Issue 3). (1993)

田中洋慶應義塾大学, 理工学部, 教授 (70011468)