慶應義塾研究者情報データベース

論文 【 表示 ／ 非表示 】

論文 【 表示 ／ 非表示 】

• A graph discretized approximation of semigroups for diffusion with drift and killing on a complete Riemannian manifold

  Ishiwata S., Kawabi H.

  Mathematische Annalen 390 （ 2 ） 2459 - 2495 2024年10月

  ISSN  00255831

  　概要を見る

  In the present paper, we prove that the C<inf>0</inf>-semigroup generated by a Schrödinger operator with drift on a complete Riemannian manifold is approximated by the discrete semigroups associated with a family of discrete time random walks with killing in a flow on a sequence of proximity graphs, which are constructed by partitions of the manifold. Furthermore, when the manifold is compact, we also obtain a quantitative error estimate of the convergence. Finally, we give examples of the partition of the manifold and the drift term on two typical manifolds: Euclidean spaces and model manifolds.

  • Access to Document (DOI)

• Stochastic quantization associated with the exp (Φ) <inf>2</inf> -quantum field model driven by space-time white noise on the torus in the full L¹ -regime

  Hoshino M., Kawabi H., Kusuoka S.

  Probability Theory and Related Fields （Probability Theory and Related Fields）  185 （ 1-2 ） 391 - 447 2023年02月

  ISSN  01788051

  　概要を見る

  The present paper is a continuation of our previous work (Hoshino et al., J Evol Equ 21:339–375, 2021) on the stochastic quantization of the exp (Φ) 2-quantum field model on the two-dimensional torus. Making use of key properties of Gaussian multiplicative chaos and refining the method for singular SPDEs introduced in the previous work, we construct a unique time-global solution to the corresponding parabolic stochastic quantization equation in the full “L1-regime” |α|<8π of the charge parameter α. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.

  • Access to Document (DOI)

• Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus

  Albeverio S., Kawabi H., Mihalache S.R., Röckner M.

  Annali Della Scuola Normale Superiore Di Pisa Classe Di Scienze 24 （ 1 ） 33 - 69 2023年

  ISSN  0391173X

  　概要を見る

  We consider space-time quantum fields with exponential/trigonometric interactions. In the context of Euclidean quantum field theory, the former and the latter are called the Høegh-Krohn model and the Sine-Gordon model, respectively. The main objective of the present paper is to construct infinite dimensional diffusion processes which solve modified stochastic quantization equations for these quantum fields on the two-dimensional torus by the Dirichlet form approach and to prove strong uniqueness of the corresponding Dirichlet operators.

  • Access to Document (DOI)

• Central Limit Theorems for Non-Symmetric Random Walks on Nilpotent Covering Graphs: Part II

  Ishiwata S., Kawabi H., Namba R.

  Potential Analysis （Potential Analysis）  55 （ 1 ） 127 - 166 2021年06月

  ISSN  09262601

  　概要を見る

  In the present paper, as a continuation of our preceding paper (Ishiwata et al. 2018), we study another kind of central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering graphs from a view point of discrete geometric analysis developed by Kotani and Sunada. We introduce a one-parameter family of random walks which interpolates between the original non-symmetric random walk and the symmetrized one. We first prove a semigroup CLT for the family of random walks by realizing the nilpotent covering graph into a nilpotent Lie group via discrete harmonic maps. The limiting diffusion semigroup is generated by the homogenized sub-Laplacian with a constant drift of the asymptotic direction on the nilpotent Lie group, which is equipped with the Albanese metric associated with the symmetrized random walk. We next prove a functional CLT (i.e., Donsker-type invariance principle) in a Hölder space over the nilpotent Lie group by combining the semigroup CLT, standard martingale techniques, and a novel pathwise argument inspired by rough path theory. Applying the corrector method, we finally extend these CLTs to the case where the realizations are not necessarily harmonic.

  • Access to Document (DOI)

• Stochastic quantization associated with the exp (Φ) <inf>2</inf> -quantum field model driven by space-time white noise on the torus

  Hoshino M., Kawabi H., Kusuoka S.

  Journal of Evolution Equations （Journal of Evolution Equations）  21 （ 1 ） 339 - 375 2021年03月

  ISSN  14243199

  　概要を見る

  We consider a quantum field model with exponential interactions on the two-dimensional torus, which is called the exp (Φ) 2-quantum field model or Høegh-Krohn’s model. In the present paper, we study the stochastic quantization of this model by singular stochastic partial differential equations, which is recently developed. By the method, we construct a unique time-global solution and the invariant probability measure of the corresponding stochastic quantization equation and identify it with an infinite-dimensional diffusion process, which has been constructed by the Dirichlet form approach.

  • Access to Document (DOI)

全件表示 >>

KOARA（リポジトリ）収録論文等 【 表示 ／ 非表示 】

KOARA（リポジトリ）収録論文等 【 表示 ／ 非表示 】

• 幾何学的視点を融合した無限次元空間上の確率解析の研究

  河備, 浩司

  科学研究費補助金研究成果報告書 2023年

• 無限次元空間上の微分作用素の確率解析的研究

  河備, 浩司

  科学研究費補助金研究成果報告書 2021年

• ベキ零被覆グラフ上の非対称ランダムウォークの長時間挙動の精密化とその応用

  河備, 浩司

  学事振興資金研究成果実績報告書 （慶應義塾大学）  2018年

• デフォルトリスクモデルに対する一考察

  河備, 浩司

  三田学会雑誌 （慶應義塾経済学会）  92 （ 3 ） 507(51) - 521(65) 1999年10月

  ISSN  00266760

競争的研究費の研究課題 【 表示 ／ 非表示 】

競争的研究費の研究課題 【 表示 ／ 非表示 】

• 幾何解析の視点を融合した無限次元空間上の確率解析の新展開

  2023年04月

  -

  2026年03月

  河備 浩司, 基盤研究(C), 補助金,  研究代表者

• 幾何学的視点を融合した無限次元空間上の確率解析の研究

  2020年04月

  -

  2023年03月

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

• 無限次元空間上の微分作用素の確率解析的研究

  2017年04月

  -

  2020年03月

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

担当授業科目 【 表示 ／ 非表示 】

担当授業科目 【 表示 ／ 非表示 】

• 微分積分

  2026年度

• 経済数学

  2026年度

• 経済数学Ⅰ

  2026年度

• 経済数学Ⅱ

  2026年度

• 微分積分入門

  2026年度

全件表示 >>