1995 Fiscal Year Annual Research Report

解析学・幾何学に関連する確率論

Research Project

Project/Area Number	07304064
Research Category	Grant-in-Aid for Co-operative Research (A)
Research Institution	Saga University
Principal Investigator	小倉幸雄佐賀大学, 理工学部, 教授 (00037847)
Co-Investigator(Kenkyū-buntansha)	谷口説男九州大学, 数理学研究科, 助教授 (70155208) 長井英生大阪大学, 基礎工学部, 教授 (70110848) 國田寛九州大学, 数理学研究科, 教授 (30022552) 渡辺信三京都大学, 理学研究科, 教授 (90025297) 池田信行立命館大学, 理工学部, 教授 (00028078)
Keywords	確率解析 / 漸近理論 / 遺伝モデル / マルコフ過程 / ディリクレ形式 / 量子カオス / 確率分布モデル / ウィナー空間
Research Abstract	以下のテーマの研究集会を開催して、講演と討論を行った。 1.「確率解析と漸近理論」:抽象ウィナー空間上の漸近理論、特に停留位相法、鞍部点法に関連する研究を主としたサーベイ形式の講演を行なった。漸近展開について、確率論、幾何学、散乱理論からの新たな問題提起がなされた。 2.「生物学にあらわれる確率モデル」:動く遺伝子の集団遺伝学等の新しい遺伝モデルの紹介、地理的構造を持つモデルの系図学についての報告があった。等数学の問題としては、無限系の時間無限大の挙動を有限系から観測可能かという問題、反応拡散モデルのスケーリング極限の問題の問題提起があった。 3.「PDE methods in Markov processes」:oblique boundary conditionが自然に現れる現象、oblique derivative problemの基本解の構成、oblique boundary condition problemをDirichlet spaceの枠組みで捉える可能性等の知見が明かにされた。 4.「量子カオスの確率論的諸問題」:エネルギーレベルでのスペクトルの漸近挙動、ランダム行列の汎関数の極限定理、量子エルゴード定理等の話題について、物理と数学の双方からの新しい結果を含むサーベイ講演と討論があった。 5.「確率分布モデルの研究」:本研究会は確率分布(族)の構成,確率分布モデルのもとでの推測問題、自然科学や人文科学におけるモデルの役割等の研究を意図して開催された。新しい分布族の提案、分布のもつ諸性質の研究、分布パラメータの推定・検定とその応用についての報告が行われた。その他に小研究集会「ウィナー空間上の確率解析」が行なわれ、Wiener空間上の非対称拡散過程の構成、Wiener空間上のLaplace作用素の摂動、Wiener汎関数積分の漸近公式等について新しい結果を含む講演があった。

Research Products
(20 results)

All Other

All Publications (20 results)

[Publications] Y.Ogura: "A probabilistic scheme for collapse of metrics." J.Math.Kyoto Univ.36. 73-92 (1996)
[Publications] Y.Hashimoto: "Short time asymptotic formula and an approximation for heat kernel of a singuar diffusion" Ito's Stochastic Calculus and Probability Theory,Springer. (to appear).
[Publications] N.Ikeda: "Levy's stochastic area formula and related problems" Proc.Symposia Pure Math., A.M.S.57. 281-305 (1995)
[Publications] S.Watanabe: "Generalized arc-sine laws for one-dimensional diffusion processes and random walks" Proc.Symposia Pure Math., A.M.S.57. 157-172 (1995)
[Publications] J.Ren: "A convergence theorem for probability densities and conditional expectations of Wiener functionas" Stochastic Processes,Proc.Intern.Conf.Beijing,Walter de Gruyter. 335-344 (1995)
[Publications] H.Kunita: "Stable limit distributions over a nilpotent Lie groups" Proc.Japan Acad.Ser A. 71. 1-5 (1995)
[Publications] H.Kunita: "Some problems concerning Le'vy processes on Lie groups" Proc.Symposia Pure Math., A.M.S.57. 323-341 (1995)
[Publications] M.Fukushima: "On reflecting diffusions on Lipschitz domains with cusps-analytic construction and Skorohod representation-" Potential Analysis. 4. 377-408 (1995)
[Publications] H.Nagai: "Bellman equations of risk sensitive control" Proceedings of the 34-th IEEE Conference on Decision and Control. 1048-1051 (1995)
[Publications] A.Bensoussan: "Some results on risk-sensitive control with full observation" Proceedings of the 34-th IEEE Conference on Decision and Control. 1657-1661 (1995)
[Publications] H.Nagai: "Bellman equations of risk sensitive control" SIAM Journal control and Optimization. 34. 74-101 (1996)
[Publications] H.Ishii: "A singular limi on risk sensitive control and semi-classical analysis" Proceedings of the seventh Japan-Russia symposium on Probability theory and Mathematical statistics. (to appear).
[Publications] S.Taniguchi: "Holomorphic functions on balls in an almost complex abstract Wiener space" J.Math.Soc.Japan. 47. 656-670 (1995)
[Publications] P.Malliavin): "Extension holomorphe des fonctionnelles analytiques defines sur un espace de Wiener reel,formule de Cauchy,phase stationnaire" C.R.Acad,Sci.Paris. 322. 261-265 (1996)
[Publications] S.Taniguchi: "On Ricci curvatures of hypersurfaces in abstract Wiener spaces" J.Funct.Anal.136. 226-244 (1996)
[Publications] K.Handa: "On a stochastic PDE related to Burger's equation with noise" IMA volumes in Mathematics and its Applications. 77. 147-156 (1995)
[Publications] H.C.Chae: "Invariant nuclear space of a second quantization operator" Hirosima Math.Journ.25. 541-559 (1995)
[Publications] N.Saitoh: "An analysis of a family of rational maps containing integrable and nonintegrable difference analogue of the Logistic equation" Journal of Physics A. (to appear).
[Publications] M.Minami: "Estimation for a common intraclass correlation in bivariate normal distributions with missing observations" Amer.J.Mathematical and Management Sci.(to appear).
[Publications] 大矢雅則他編: "数理情報科学事典" 朝倉書店, 1164 (1995)

1995 Fiscal Year Annual Research Report

解析学・幾何学に関連する確率論

Principal Investigator

小倉 幸雄 佐賀大学, 理工学部, 教授 (00037847)

Research Products

[Publications] Y.Ogura: "A probabilistic scheme for collapse of metrics." J.Math.Kyoto Univ.36. 73-92 (1996)

[Publications] Y.Hashimoto: "Short time asymptotic formula and an approximation for heat kernel of a singuar diffusion" Ito's Stochastic Calculus and Probability Theory,Springer. (to appear).

[Publications] N.Ikeda: "Levy's stochastic area formula and related problems" Proc.Symposia Pure Math., A.M.S.57. 281-305 (1995)

[Publications] S.Watanabe: "Generalized arc-sine laws for one-dimensional diffusion processes and random walks" Proc.Symposia Pure Math., A.M.S.57. 157-172 (1995)

[Publications] J.Ren: "A convergence theorem for probability densities and conditional expectations of Wiener functionas" Stochastic Processes,Proc.Intern.Conf.Beijing,Walter de Gruyter. 335-344 (1995)

[Publications] H.Kunita: "Stable limit distributions over a nilpotent Lie groups" Proc.Japan Acad.Ser A. 71. 1-5 (1995)

[Publications] H.Kunita: "Some problems concerning Le'vy processes on Lie groups" Proc.Symposia Pure Math., A.M.S.57. 323-341 (1995)

[Publications] M.Fukushima: "On reflecting diffusions on Lipschitz domains with cusps-analytic construction and Skorohod representation-" Potential Analysis. 4. 377-408 (1995)

[Publications] H.Nagai: "Bellman equations of risk sensitive control" Proceedings of the 34-th IEEE Conference on Decision and Control. 1048-1051 (1995)

[Publications] A.Bensoussan: "Some results on risk-sensitive control with full observation" Proceedings of the 34-th IEEE Conference on Decision and Control. 1657-1661 (1995)

[Publications] H.Nagai: "Bellman equations of risk sensitive control" SIAM Journal control and Optimization. 34. 74-101 (1996)

[Publications] H.Ishii: "A singular limi on risk sensitive control and semi-classical analysis" Proceedings of the seventh Japan-Russia symposium on Probability theory and Mathematical statistics. (to appear).

[Publications] S.Taniguchi: "Holomorphic functions on balls in an almost complex abstract Wiener space" J.Math.Soc.Japan. 47. 656-670 (1995)

[Publications] P.Malliavin): "Extension holomorphe des fonctionnelles analytiques defines sur un espace de Wiener reel,formule de Cauchy,phase stationnaire" C.R.Acad,Sci.Paris. 322. 261-265 (1996)

[Publications] S.Taniguchi: "On Ricci curvatures of hypersurfaces in abstract Wiener spaces" J.Funct.Anal.136. 226-244 (1996)

[Publications] K.Handa: "On a stochastic PDE related to Burger's equation with noise" IMA volumes in Mathematics and its Applications. 77. 147-156 (1995)

[Publications] H.C.Chae: "Invariant nuclear space of a second quantization operator" Hirosima Math.Journ.25. 541-559 (1995)

[Publications] N.Saitoh: "An analysis of a family of rational maps containing integrable and nonintegrable difference analogue of the Logistic equation" Journal of Physics A. (to appear).

[Publications] M.Minami: "Estimation for a common intraclass correlation in bivariate normal distributions with missing observations" Amer.J.Mathematical and Management Sci.(to appear).

[Publications] 大矢雅則他編: "数理情報科学事典" 朝倉書店, 1164 (1995)

小倉幸雄佐賀大学, 理工学部, 教授 (00037847)