種村 秀紀 (タネムラ ヒデキ)

Tanemura, Hideki

写真a

所属(所属キャンパス)

理工学部 数理科学科 (矢上)

職名

教授

経歴 【 表示 / 非表示

  • 2018年04月
    -
    継続中

    慶應義塾大学, 理工学部, 教授

  • 1989年09月
    -
    1994年01月

    千葉大学, 理学部, 助手

  • 1994年02月
    -
    2005年11月

    千葉大学, 理学部, 助教授

  • 2005年12月
    -
    2018年03月

    千葉大学, 理学部, 教授

学歴 【 表示 / 非表示

  • 1978年04月
    -
    1982年03月

    慶應義塾大学, 工学部, 数理工学科

    大学, 卒業

  • 1982年04月
    -
    1984年03月

    慶應義塾大学, 工学研究科, 数理工学

    大学院, 修了, 博士前期

  • 1984年04月
    -
    1989年03月

    慶應義塾大学, 理工学研究科, 数理科学専攻

    大学院, 修了, 博士後期

  • 1989年04月
    -
    1989年08月

    慶應義塾大学, 理工学研究科, 数理科学専攻

    その他, その他

学位 【 表示 / 非表示

  • 理学博士, 慶應義塾大学, 1989年03月

 

論文 【 表示 / 非表示

  • Infinite-dimensional stochastic differential equations and tail σ-fields II: the IFC condition

    Kawamoto Y., Osada H., Tanemura H.

    Journal of the Mathematical Society of Japan (Journal of the Mathematical Society of Japan)  74 ( 1 ) 79 - 128 2022年

    ISSN  00255645

     概要を見る

    In a previous report, the second and third authors gave general theorems for unique strong solutions of infinite-dimensional stochastic differential equations (ISDEs) describing the dynamics of infinitely many interacting Brownian particles. One of the critical assumptions is the “IFC” condition. The IFC condition requires that, for a given weak solution, the scheme consisting of the finite-dimensional stochastic differential equations (SDEs) related to the ISDEs exists. Furthermore, the IFC condition implies that each finite-dimensional SDE has unique strong solutions. Unlike other assumptions, the IFC condition is challenging to verify, and so the previous report only verified it for solutions given by quasi-regular Dirichlet forms. In the present paper, we provide a sufficient condition for the IFC requirement in more general situations. In particular, we prove the IFC condition without assuming the quasi-regularity or symmetry of the associated Dirichlet forms. As an application of the theoretical formulation, the results derived in this paper are used to prove the uniqueness of Dirichlet forms and the dynamical universality of random matrices.

  • Uniqueness of Dirichlet Forms Related to Infinite Systems of Interacting Brownian Motions

    Kawamoto Y., Osada H., Tanemura H.

    Potential Analysis (Potential Analysis)  55 ( 4 ) 639 - 676 2021年12月

    ISSN  09262601

     概要を見る

    The Dirichlet forms related to various infinite systems of interacting Brownian motions are studied. For a given random point field μ, there exist two natural infinite-volume Dirichlet forms (Eupr, Dupr) and (Elwr, Dlwr) on L2(S,μ) describing interacting Brownian motions each with unlabeled equilibrium state μ. The former is a decreasing limit of a scheme of such finite-volume Dirichlet forms, and the latter is an increasing limit of another scheme of such finite-volume Dirichlet forms. Furthermore, the latter is an extension of the former. We present a sufficient condition such that these two Dirichlet forms are the same. In the first main theorem (Theorem 3.1) the Markovian semi-group given by (Elwr, Dlwr) is associated with a natural infinite-dimensional stochastic differential equation (ISDE). In the second main theorem (Theorem 3.2), we prove that these Dirichlet forms coincide with each other by using the uniqueness of weak solutions of ISDE. We apply Theorem 3.1 to stochastic dynamics arising from random matrix theory such as the sine, Bessel, and Ginibre interacting Brownian motions and interacting Brownian motions with Ruelle’s class interaction potentials, and Theorem 3.2 to the sine2 interacting Brownian motion and interacting Brownian motions with Ruelle’s class interaction potentials of C03-class.

  • Infinite-dimensional stochastic differential equations and tail σ -fields

    Osada H., Tanemura H.

    Probability Theory and Related Fields (Probability Theory and Related Fields)  177 ( 3-4 ) 1137 - 1242 2020年08月

    ISSN  01788051

     概要を見る

    We present general theorems solving the long-standing problem of the existence and pathwise uniqueness of strong solutions of infinite-dimensional stochastic differential equations (ISDEs) called interacting Brownian motions. These ISDEs describe the dynamics of infinitely-many Brownian particles moving in Rd with free potential Φ and mutual interaction potential Ψ. We apply the theorems to essentially all interaction potentials of Ruelle’s class such as the Lennard-Jones 6-12 potential and Riesz potentials, and to logarithmic potentials appearing in random matrix theory. We solve ISDEs of the Ginibre interacting Brownian motion and the sineβ interacting Brownian motion with β= 1 , 2 , 4. We also use the theorems in separate papers for the Airy and Bessel interacting Brownian motions. One of the critical points for proving the general theorems is to establish a new formulation of solutions of ISDEs in terms of tail σ-fields of labeled path spaces consisting of trajectories of infinitely-many particles. These formulations are equivalent to the original notions of solutions of ISDEs, and more feasible to treat in infinite dimensions.

KOARA(リポジトリ)収録論文等 【 表示 / 非表示

競争的研究費の研究課題 【 表示 / 非表示

  • 無限粒子系における相転移現象の確率解析

    2019年04月
    -
    2024年03月

    文部科学省・日本学術振興会, 科学研究費助成事業, 種村 秀紀, 基盤研究(B), 補助金,  研究代表者

 

担当授業科目 【 表示 / 非表示

  • 確率特論A

    2022年度

  • 生命保険数学特論(OLIS生命保険寄附講座)

    2022年度

  • 確率論第1同演習

    2022年度

  • 数学1B

    2022年度

  • 数学1A

    2022年度

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