メイン＞研究室紹介＞岡部ゼミ＞業績等

業績等；岡部教授

著書

[1] 確率過程 応用と話題, 4章 定常解析と因果解析 (pp.118-pp.139), 情報理論とその応用シリーズ 2, 情報理論とその応用学会編, 培風館, 1994.

[2] 時系列解析における揺動散逸原理と実験数学, 日本評論社, 2002年2月.

[3] 確率・統計，応用数学基礎講座6, 朝倉書店, 2002年3月.

[4] 数理工学への誘い，12章 時系列解析と揺動散逸原理(pp.123-pp.137), 東京大学工学部計数工学科数理情報工学コース編，日本評論社，2002年9月.

[5] 実験数学---地震波，オーロラ，脳波，音声の時系列解析---，朝倉書店，2005年11月.

学術雑誌

[1] 岡部靖憲, Kolmogorov の拡張定理について, 数学 20 (1968), 222-225.

[2] Yasunori Okabe, On the boundary system in the boundary problem for Markov processes, USSR-Japan Symposium on Probability Theory, Habarovsk, August, 1969, 282-300.

[3] Yasunori Okabe, The resolution of an irregularity of boundary points in the boundary problem for Markov processes,  J. Math. Soc. Japan, 22 (1970), 47-104.

[4] Yasunori Okabe and Shinnichi Kotani, On a Markovian property of stationary Gaussian processes with a multi-dimensional parameter,  Hyperfunctions and Pseudo-Differential Equations,  Lecture Notes in Math., Vol. 287, Springer, Berlin, 1973, 153-163.

[5] Yasunori Okabe, On a Markovian property of Gaussian processes,  Proc. of the Second Japan-USSR Symposium on Probability Theory, Lecture Notes in Math., Vol.330, Springer, Berlin, 1973, 83-98.

[6] Yasunori Okabe, Stationary Gaussian processes with Markovian property and M. Sato's hyperfunctions, Japanese J. Math., 41 (1973), 69-122.

[7] 岡部靖憲・小谷真一, 正規過程のマルコフ性と局所性について, 数学 25 (1973), 266-272.

[8] Yasunori Okabe, On the structure of splitting fields of stationary Gaussian processes with finite multiple Markovian property, Nagoya Math. J., 54 (1974), 191-213.

[9] Yasunori Okabe and  Akinobu Shimizu, On the pathwise uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ., 15 (1975), 455-466.

[10] Yasunori Okabe, On stationary linear processes with Markovian property, Proc. of the Third Japan-USSR Symposium on Probability Theory, Lecture Notes in Math., Vol.550, Springer, Berlin, 1976, 461-466.

[11] Yasunori Okabe, On the germ fields of stationary Gaussian processes with Markovian property, J. Math. Soc. Japan, 28 (1976), 86-95.

[12] Yasunori Okabe, Innovation processes associated with stationary Gaussian processes with application to the problem of prediction, Nagoya Math. J., 70 (1978), 81-104.

[13] Yasunori Okabe, On a stationary Gaussian process with T-positivity and its associated Langevin equation and S-Matrix, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 26 (1979), 115-165.

[14] 岡部靖憲, Langevin 方程式について，数学 33 (1981), 306-324.

[15] Yasunori Okabe, On a stochastic differential equation for a stationary Gaussian process  with T-positivity and the fluctuation-dissipation theorem, J. Fac. Sci. Univ. Tokyo, Sec. IA, 28 (1981), 169-213.

[16] Yasunori Okabe, On a stochastic differential equation for a stationary Gaussian process  with finite multiple Markovian property and the fluctuation-dissipation theorem, J. Fac. Sci. Univ. Tokyo, Sec. IA, 28 (1982), 793-804.

[17] Yasunori Okabe, On a wave equation associated with prediction errors for a stationary Gaussian process, Lecture Notes in Control and Information Sciences, Vol. 49, 1983, 215-226.

[18] Yuji Nakano and Yasunori Okabe, On a multi-dimensional [alpha, beta, gamma]-Langevin equation, Proc. Japan Acad., 59 (1983), 171-173.

[19] Yuji Nakano and Yasunori Okabe, On a 2-dimensional [alpha, beta, gamma]-Langevin equation, Proc. of the Fourth Japan-USSR Symposium on Probability Theory, Lecture Notes in Math., Vol.1021, Springer, Berlin, 1983, 481-485.

[20] Yasunori Okabe, A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process, Commun. Math. Phys., 98 (1985), 449-468.

[21] Yasunori Okabe, On KMO-Langevin equations for stationary Gaussian processes with T-positivity, J. Fac. Sci. Univ. Tokyo, Sect. IA. Math., 33 (1986), 1-56.

[22] Yasunori Okabe, KMO-Langevin equation and fluctuation-dissipation theorem (I), Hokkaido Math. J., 15 (1986), 163-216.

[23] Yasunori Okabe, KMO-Langevin equation and fluctuation-dissipation theorem (II), Hokkaido Math. J., 15 (1986), 317-355.

[24] Yasunori Okabe, On the theory of the Brownian motion with the Alder-Wainwright effect, J. Stat. Phys., 45 (1986), 953-981.

[25] Yasunori Okabe, Stokes-Boussisesq-Langevin equation and fluctuation-dissipation theorem, Proc. of the IV Vilnius Conference on Probability Theory and Mathematical Statistics, VNU Science Press, 1986, 431-436.

[26] Yasunori Okabe, On the theory of discrete KMO-Langevin equations with reflection positivity (I), Hokkaido Math. J., 16 (1987), 315-341.

[27] Yasunori Okabe, On the theory of discrete KMO-Langevin equations with reflection positivity (II), Hokkaido Math. J., 17 (1988), 1-44.

[28] Yasunori Okabe, On the theory of discrete KMO-Langevin equations with reflection positivity (III), Hokkaido Math. J., 18 (1989), 149-174.

[29] Yasunori Okabe, On a stochastic difference equation for the multi-dimensional weakly stationary process with discrete time, lqlq Algebraic Analysis"  in celebration of Professor M. Sato's sixtieth birthday, Prospect of Algebraic Analysis (ed. by Masaki Kashiwara and Takashi Kawai), Academic Press, 1988, 601-645.

[30] Yasunori Okabe, On long time tails of correlation functions for KMO-Langevin equations, Proc. of the Fifth Japan-USSR Symposium on Probability Theory, Kyoto, July, Lecture Notes in Math., Springer, 1986, Vol.1299, 391-397.

[31] 岡部靖憲, 非線型予測理論と因果解析, システム／制御／情報、lceil非線型システム特集号rceil, 33巻,linebreak 9号, 1989, 478-487.

[32] Yasunori Okabe, Langevin equation and fluctuation-dissipation theorem, Stochastic Processes and their Applications(ed. by S. Albeverio et al.), Kluwer Academic Publishers, 1990, 275-299.

[33] Yasunori Okabe and Yuji Nakano, The theory of KM_2O-Langevin equations and its applications to data analysis (I): Stationary analysis, Hokkaido Math. J., 20 (1991), 45-90.

[34] Yasunori Okabe, The random forces associated with discrete-time weakly stationary processes, Proc. of  Preseminar for International Conference on Gaussian Random  Fields (ed. by T. Hida and K. Saithat o), Nagoya, 1991, 126-134.

[35] 岡部靖憲, Langevin 方程式と因果解析, 数学 43 (1991), 322-346.

[36] Yasunori Okabe and  Akihiko Inoue, On the exponential decay of the correlation functions for KMO-Langevin equations, Japanese J. Math., 18 (1992), 13-24.
[37] Yasunori Okabe, Application of the theory of KM_2O-Langevin equations to the linear prediction problem for the multi-dimensional weakly stationary time series, J. Math. Soc. Japan, 45 (1993), 277-294.

[38] Yasunori Okabe, A new algorithm derived from the view-point of the fluctuation-dissipation principle in the theory of KM_2O-Langevin equations, Hokkaido Math, J., 22 (1993), 199-209.

[39] Yasunori Okabe and Akihiko Inoue, The theory of  KM_2O-Langevin equations and its applications to data analysis (II): Causal analysis (1), Nagoya Math. J., {bf 134}(1994), 1-28.

[40] Yasunori Okabe, Hajime Mano and Yoshiaki Itoh, Random collision model for interacting populations of two species and the fluctuation-dissipation theorem---the law of large numbers and the central limit theorem, Hokkaido Math. J., Vol.23  No.3., 507-522.

[41] Yasunori Okabe, Langevin equation and causal analysis, Amer. Math. Soc. Transl., 16 (1994), 19-50.

[42] Yasunori Okabe and Takashi Ootsuka, Application of the theory of KM_2O-Langevin equations to the non-linear prediction problem for the one-dimensional strictly stationary time series,J. Math. Soc. Japan, 47-2(1995), 349-367.

[43] Yukio Kiho, Tsuruji Iwai, Toshihiko Migita, Yoshio Okada, M.J.A., Yasunori Okabe, Mariko Ochi and Kaoru Katori, Functional Word in a Protein III. Syntax and Energies, Proc. of Japan Acad. 72-5(1996), 95-100.

[44] Yukio Kiho, Aiko Ubasaswa, Yasunori Okabe and Tsuruji Iwai, Functional Word in a Protein IV.Alphabet, Proc. of Japan Acad. 72-9(1996), 185-190.

[45] Yukio Kiho, Ryuich Yamada, Yasunori Okabe, Chiristopher Palmer and Yoshio Okada, M.J.A., Application of the Jellyfish Model I. Virulency of Some Mammalian Viruses, Proc.of Japan Acad., 73-8(1997), 170-175.

[46] Yasunori Okabe, Nonlinear time series analysis based upon the fluctuation-dissipation theorem, Nonlinear Analysis, Theory, Methods & Applications, 30(1997), 2249-2260.

[47] Yasunori Okabe, On a Kubo noise associated with a multidimensional stationary curve in a Hilbert space, in celebration of Professor Hiroshi Ezawa's  sixty-five birthday, 1997, 1-8.

[48] Yasunori Okabe and Takashi Yamane, The theory of KM_2O-Langevin equations and its applications to data analysis rm{(III)}: deterministic analysis, Nagoya Math. J., 152(1998), 175-201.

[49] Takashi Kanamaru, Takehiko Horita and Yasunori Okabe, Stochastic resonance in the Hodgkin-Huxley net work, Jounal of the Physical Society of Japan, Vol.67, No.12, December, 1998, 4058-4063.

[50] 関本勝也・岡部靖憲・緒方純俊, 隣接する地域間における大気汚染物質濃度の相互因果解析, 計測自動制御学会論文集, 35-12(1999), 1524-1529.

[51] Yasunori Okabe, On the theory of KM_2O-Langevin equations for stationary flows (I): characterization theorem, J. Math. Soc. Japan, 51-4(1999), 817-841.

[52] Yasunori Okabe, On the theory of KM_2O-Langevin equations for stationary flows (II): construction theorem, Acta Applicandae Mathematicae, 63(2000), 307-322.

[53] Yasunori Okabe and Masaya Matsuura, On the theory of KM_2O-Langevin equations for stationary flows (III): extension theorem, Hokkaido Math. J., 29(2000), 369-382.

[54] Yasunori Okabe and Akihito Kaneko, On a non-linear prediction analysis for multi-dimensional stochastic processes with its applications to data analysis, Hokkaido Math. J., 29(2000), 601-657.

[55] Masaya Sekimoto, Takahiro Kawakami, Yasunori Okabe and Sumiyoshi Ogata, Strange periodic changes in walking EEG and estimation of EEG's deteriministic structure in short time series, International Journal of Chaos Theory and Applications, 5(2000), 63-71.

[56] Masaya Sekimoto, Yasunori Okabe and Sumiyoshi Ogata, Recognition of non-linear, deterministic structures of Japanese vowels by causal analysis, International Journal of Chaos Theory and Applications, 6(2001), 55-69.

[57] Naoki Masuda and Yasunori Okabe, Time series analysis with wavelet coefficients, Japan J. Ind. Applied Math., 18(2001), 131-160.

[58] Masaya Matsuura and Yasunori Okabe, On a non-linear prediction problem for one-dimensional stochastic processes, Japan J . of Mathematics,  21(2001), 51-112.

[59] Maciej Klimek, Erlendur Karlson, Masaya Matsuura and Yasunori Okabe,  A geometric proof of the fluctuation-dissipation theorem for the KM_2O-Langevin equations, Hokkaido Mathematical Journal, 29(2002), 615-628.

[60] Yasunori Okabe, Masaya Matsuura and Maciej Klimek, On a method for detecting certain signs of stock market crashes by non-linear stationary test, International Journal of Pure and Applied Mathematics, 3(2002), 443-484.

[61] Masaya Matsuura and Yasunori Okabe, On the theory of KM_2O-Langevin equations for non-stationary and degenerate flows, J. Math. Soc. Japan, 55(2003), 523-563.

[62] 加藤天美・平田雅之・江田英樹・真渓歩・水野由子・篠崎和弘・岡部靖憲・柳田敏雄・吉崎俊樹, 脳−コンピュータインターフェイス，神経研究の進歩，第48巻，第6号，2004年12月10日，医学書院, 872-882.

[63] Yasunori Okabe and Masaya Matsuura, On non-linear filtering problems for discrete time stochastic processes, J. Math. Soc. Japan, 57(2005), 1067-1076.

[64] Yasunori Okabe and Masaya Matsuura, Chaos and KM_2O-Langevin equations, Bulletin of Informatics and and Cybenetics, 37(2005), 73-107.

[65] Minoru Takeo, Hiroko Ueda, Yasunori Okabe and Masaya Matsuura, Waveform characteristics of deep low-frequency earthquakes: Time series evolution based on the theory of KM_2O-Langevin equations, Geophysical Journal International, 165(2006), 87-107.

[66] Yasunori Okabe, On a KM_2O-Langevin equation with continuous time (I), J. Math. Sci. Unive. Tokyo, 13(2006), 545-593.

[67] Kenjiro Suzuki, Yasunori Okabe  and Takaaki Fujii, On a non-linear risk analysis for stock market indexes, to appear in JAFEE.

[68] Yasunori Okabe, Masaya Matsuura, Minoru Takeo and Hiroko Ueda, On an abnormality test for detecting certain signs of earthquakes, to be submitted is Geophysical Journal International.

[69] Maciej Klimek, Masaya Matsuura and Yasunori Okabe, Degenerate non-stationary flows and finite block frames, to be submitted in J. Functional Analysis and Applications.

[70] Yasunori Okabe and Kazuo Murota, On a combinatorial property of Dirichlet forms and Green forms associated with Markov chains (1), to be submitted in Osaka J. Math.

講究録

[1] マルコフ過程に対するlateral condition, 数理解析研究所講究録57, 京都大学数理解析研究所, 1968年11月，78-103.

[2] マルコフ過程の境界問題における境界点のirregularityの解消, 函数解析的方法による解析学の諸問題の研究報告集, 1969年3月，東京.

[3] マルコフ過程論，数理解析研究所講究録112, 京都大学数理解析研究所，1971年2月，177-192.

[4] 超函数理と偏微分方程式の理論, 数理解析研究所講究録145, 京都大学数理解析研究所, 1972年5月，48-60.

[5] 多重マルコフ性と予測理論への応用，数理解析研究所講究録151, 京都大学数理解析研究所，1972年10月，67-75.

[6] 超函数と解析汎函数の理論と応用，数理解析研究所講究録162, 京都大学数理解析研究所，1972年10月，67-75.

[7] 代数解析とその応用，数理解析研究所講究録226, 京都大学数理解析研究所，1975年2月，21-28.

[8] SEMINAR ON PROBABILITY, Vol.47 4月シンポジウム(1977)報告集, 正規定常過程のT-正値性とマルコフ性-Langevin equation-他7偏，1977年，確率論セミナー, 29-70.

[9] 偏微分方程式の解の構造, 数理解析研究所講究録337, 1976・1977年合併号， 京都大学数理解析研究所，1978年11月，211-222.

[10] 確率過程論と開放系の統計力学, 数理解析研究所講究録367, 京都大学数理解析研究所，1979年10月，94-113.

[11] 確率過程論と開放系の統計力学，数理解析研究所講究録434, 京都大学数理解析研究所, 1981年8月，154-182.

[12] 代数解析学の展望，数理解析研究所講究録675, 京都大学数理解析研究所，1988年12月, 47-57.

[13] 非線形現象のシステム設計と予測解析の確率過程論的研究，統計数理研究所共同研究リポート59,　統計数理研究所，1994年3月，1-26.

解説論文, 総合報告

[1] 測度と非負線型汎函数とその応用(I), 卒業記念論文随筆集 aleph_0，東大理学部数学科卒業生，1966年度, 1-40.

[2] 確率論とポテンシャル論，ノート: 最近の日本の数学（そのＶ）河田敬義編, 数学 26 (1974), 157-159.

[3] ブラウン運動と佐藤の超函数， aleph_1, 1970年10月，56-70.

[4] ランジュヴァン方程式と弦の振動方程式，aleph_2, 1978年4月，161-170.

[5] 揺動散逸定理，数理科学，特集「確率過程」，1981年6月号, 26-33.

[6] 時系列とKM_2O-ランジュヴァン方程式の理論, BASIC数学特集「確率論展望（上）」, 1989年2月号, 38-43.

[7] チャップマン--コルモゴロフの方程式, 数学セミナー増刊「数学cdot物理100の方程式 -- 連立方程式から数理物理の最先端へ」, 日本評論社，1989年４月, 118-119.

[8] 前進cdot後退方程式, 数学セミナー増刊「数学cdot物理100の方程式---連立方程式から数理物理の最先端へ」, 日本評論社，1989年４月, 120-121.

[9] 確率微分方程式, 数学セミナー増刊「数学cdot物理100の方程式---連立方程式から数理物理の最先端へ」, 日本評論社，1989年４月, 122-123.

[10] KMO-ランジュヴァン方程式とEinsteinの関係式について,
非平衡系統計力学の基礎研究懇話会, 物性研究 52-3 (1989-6), 221-234.

[11] 揺動散逸原理, 数学セミナー, 1990年6月号, 52-53.

[12] Langevin 方程式と因果解析, 1990年9月, 電子情報通信学会, 39-46.

[13] 揺動散逸定理, 数理科学, 別冊「数理物理の展開--数学と物理のタピストリー」, 1990年10月, 100-108.

[14] 自然科学と定常過程, 数理科学, 特集「確率的自然像」, 1991年10月号, 21-28.

[15] 確率過程の特徴付け -- 定性的性質からモデルへ, 数理科学,
特集「数理物理の歩み」, 1992年5月号, 11-17.

[16] 確率論の公理化, 数学セミナー特集「その概念によって何が変わったか」, 1993年1月号, 20-21.

[17] 往復書簡: 純粋数学vs応用数学, 砂田利一・岡部靖憲, 数学セミナー, 1994年4月号 -- 1995年3月号.

[18] 実験数学と般若心経,　aleph_3,　1995年3月，1-10.

[19] 座談会「数物学会の分離と二つの科学」，特集「日本物理学会50周年記念」，日本物理学会誌，Vol.51, No.1, (1996), 26-36.

[20] 複雑系と実験数学, 特集/数学−絵物語，数学セミナー，1997年5月, 14-15.

[21] カオスの確率過程論と実験数学, カオス研究の最前線 -- その７, 数理科学, 1997年7月号, 54-62.