Updated on 2025/06/09

Information

 

写真a

 
INAHAMA YUZURU
 
Organization
Faculty of Mathematics Division of Analysis Professor
School of Sciences Department of Mathematics(Concurrent)
Graduate School of Mathematics Department of Mathematics(Concurrent)
Title
Professor
Contact information
メールアドレス
Profile
I am studying and teaching mathematics, in particular, probability theory.
External link

Degree

  • Doctor of Science

Research History

  • 名古屋大学 (2009年4月ー2015年10月) 東京工業大学 (2006年2月ー2009年3月)   

Research Interests・Research Keywords

  • Research theme: probability theory

    Keyword: rough path theory, Malliavin calculus, stochastic differential equation.

    Research period: 1995.4 - 2026.12

Papers

  • Malliavin differentiability of solutions of rough differential equations Reviewed International journal

    稲濱 譲

    Journal of Functional Analysis   267   1566 - 1584   2016.10

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    Language:English   Publishing type:Research paper (scientific journal)  

    In this paper we study rough differential equations
    driven by Gaussian rough paths from the viewpoint of Malliavin calculus.
    Under mild assumptions on coefficient vector fields and underlying Gaussian processes,
    we prove that solutions at a fixed time is smooth in the sense of Malliavin calculus.
    Examples of Gaussian processes include fractional Brownian motion with Hurst parameter larger than 1/4.

  • Moderate Deviations for Two-Time Scale Systems with Mixed Fractional Brownian Motion

    Yang, XY; Inahama, Y; Xu, Y

    APPLIED MATHEMATICS AND OPTIMIZATION   90 ( 1 )   2024.8   ISSN:0095-4616 eISSN:1432-0606

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    Publisher:Applied Mathematics and Optimization  

    This work focuses on moderate deviations for two-time scale systems with mixed fractional Brownian motion. Our proof uses the weak convergence method which is based on the variational representation formula for mixed fractional Brownian motion. Throughout this paper, the Hurst parameter of fractional Brownian motion is larger than 1/2 and the integral along the fractional Brownian motion is understood as the generalized Riemann-Stieltjes integral. First, we consider single-time scale systems with fractional Brownian motion. The key of our proof is showing the weak convergence of the controlled system. Next, we extend our method to show moderate deviations for two-time scale systems. To this goal, we combine the Khasminskii-type averaging principle and the weak convergence approach.

    DOI: 10.1007/s00245-024-10159-w

    Web of Science

    Scopus

  • Moderate deviations for rough differential equations

    Inahama, Y; Xu, Y; Yang, XY

    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY   56 ( 8 )   2738 - 2748   2024.8   ISSN:0024-6093 eISSN:1469-2120

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    Publisher:Bulletin of the London Mathematical Society  

    Small noise problems are quite important for all types of stochastic differential equations. In this paper, we focus on rough differential equations driven by scaled fractional Brownian rough path with Hurst parameter (Formula presented.). We prove a moderate deviation principle for this equation as the scale parameter tends to zero.

    DOI: 10.1112/blms.13097

    Web of Science

    Scopus

  • Support theorem for pinned diffusion processes Reviewed International journal

    @Yuzuru Inahama

    Nagoya Mathematical Journal   253   241 - 264   2024.1   ISSN:0027-7630 eISSN:2152-6842

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Nagoya Mathematical Journal  

    In this paper we prove a support theorem of Stroock-Varadhan type for pinned diffusion processes.To this end we use two powerful results from stochastic analysis.One is quasi-sure analysis for Brownian rough path. The other is Aida-Kusuoka-Stroock's positivity theorem for the densities of weighted laws of non-degenerate Wiener functionals.

    DOI: 10.1017/nmj.2023.25

    Web of Science

    Scopus

    Repository Public URL: https://hdl.handle.net/2324/7173583

  • Large Deviations for Small Noise Hypo elliptic Diffusion Bridges on Sub-Riemannian Manifolds

    Inahama, Y

    PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES   60 ( 1 )   145 - 184   2024   ISSN:0034-5318 eISSN:1663-4926

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    Publisher:Publications of the Research Institute for Mathematical Sciences  

    In this paper we study a large deviation principle of Freidlin–Wentzell type for pinned hypoelliptic diffusion measures associated with a natural sub-Laplacian on a compact sub-Riemannian manifold. To prove this large deviation principle, we use rough path theory and manifold-valued Malliavin calculus.

    DOI: 10.4171/PRIMS/60-1-4

    Web of Science

    Scopus

  • Averaging principles for mixed fast-slow systems driven by fractional Brownian motion

    Pei, B; Inahama, Y; Xu, Y

    KYOTO JOURNAL OF MATHEMATICS   63 ( 4 )   721 - 748   2023.11   ISSN:2156-2261 eISSN:2154-3321

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    Publisher:Kyoto Journal of Mathematics  

    We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Itô integral, and the integral with respect to fBm is a generalized Riemann- Stieltjes integral by means of fractional calculus.We establish an averaging principle in which the fast-varying diffusion process of the fast-slow systems acts as a "noise"to be averaged out in the limit.We show that the slow process has a limit in the mean square sense, which is characterized by the solution of stochastic differential equations driven by fBm whose coefficients are averaged with respect to the stationary measure of the fast-varying diffusion. An implication is that one can ignore the complex original systems and concentrate on the averaged systems instead. This averaging principle paves the way for reduction of computational complexity.

    DOI: 10.1215/21562261-2023-0001

    Web of Science

    Scopus

  • SUPPORT THEOREM FOR PINNED DIFFUSION PROCESSES

    INAHAMA YUZURU

    Nagoya Mathematical Journal   253   241 - 264   2023.9   ISSN:00277630 eISSN:21526842

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    Language:English   Publisher:Cambridge University Press  

    In this paper, we prove a support theorem of Stroock–Varadhan type for pinned diffusion processes. To this end, we use two powerful results from stochastic analysis. One is quasi-sure analysis for Brownian rough path. The other is Aida–Kusuoka–Stroock’s positivity theorem for the densities of weighted laws of non-degenerate Wiener functionals.

    CiNii Research

  • Averaging principle for fast-slow system driven by mixed fractional Brownian rough path (vol 301, pg 202, 2021)

    Pei, B; Inahama, Y; Xu, Y

    JOURNAL OF DIFFERENTIAL EQUATIONS   355   437 - 440   2023.5   ISSN:0022-0396 eISSN:1090-2732

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    Publisher:Journal of Differential Equations  

    DOI: 10.1016/j.jde.2023.02.039

    Web of Science

    Scopus

  • Positivity of the Density for Rough Differential Equations

    Inahama, Y; Pei, B

    JOURNAL OF THEORETICAL PROBABILITY   35 ( 3 )   1863 - 1877   2022.9   ISSN:0894-9840 eISSN:1572-9230

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    Publisher:Journal of Theoretical Probability  

    Due to recent developments of Malliavin calculus for rough differential equations, it is now known that, under natural assumptions, the law of a unique solution at a fixed time has a smooth density function. Therefore, it is quite natural to ask whether or when the density is strictly positive. In this paper we study this problem from the viewpoint of Aida–Kusuoka–Stroock’s general theory.

    DOI: 10.1007/s10959-021-01116-2

    Web of Science

    Scopus

  • Positivity of the Density for Rough Differential Equations Reviewed International journal

    Yuzuru Inahama, Pei Bin

    Journal of Theoretical Probability   35   1863 - 1877   2022.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: https://doi.org/10.1007/s10959-021-01116-2

  • Averaging principle for fast-slow system driven by mixed fractional Brownian rough path Reviewed International journal

    Bin Pei, Yuzuru Inahama, Yong Xu

    J. Differential Equations   301   202 - 235   2021.11

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: https://doi.org/10.1016/j.jde.2021.08.006

  • Paracontrolled quasi-geostrophic equation with space-time white noise Reviewed International journal

    Yuzuru Inahama, Yoshihiro Sawano.

    Dissertationes Math.   558 ( 35 )   1 - 81   2020.8

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    Language:English   Publishing type:Research paper (scientific journal)  

    We study the stochastic dissipative quasi-geostrophic equation with space-time white noise on the two-dimensional torus.
    This equation is highly singular and basically ill-posed in its original form.
    The main objective of the present paper is to formulate and solve this equation locally in time in the framework of paracontrolled calculus
    when the differential order of the main term, the fractional Laplacian, is larger than $7/4$. No renormalization has to be done for this model.

  • Stochastic flows and rough differential equations on foliated spaces Reviewed International journal

    Yuzuru Inahama, Kiyotaka Suzaki

    Bull. Sci. Math.   160   2020.3

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Rough path theory and stochastic analysis Invited Reviewed International journal

    Yuzuru Inahama

    Sugaku Expositions   32 ( 1 )   113 - 136   2019.1

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Stochastic complex Ginzburg-Landau equation with space-time white noise Reviewed International journal

    Masato Hoshino, Yuzuru Inahama, Nubuaki Naganuma,

    Electron. J. Probab.   no. 22 ( Paper no. 104 )   2017.6

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Short time full asymptotic expansion of hypoelliptic heat kernel at the cut locus Reviewed International journal

    Yuzuru Inahama, Setsuo Taniguchi

    Forum Math. Sigma   5 ( e16 )   2017.6

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion Reviewed International journal

    Yuzuru Inahama

    Electron. J. Probab.   no. 21 ( Paper no. 34 )   2016.6

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Large deviations for rough path lifts of Watanabe's pullbacks of delta functions Reviewed International journal

    Yuzuru Inahama

    Int. Math. Res. Not.   IMRN 2016 ( no. 20 )   6378 - 6414   2016.6

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    Language:English   Publishing type:Research paper (scientific journal)  

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Books

  • ラフパス理論と確率解析

    稲濱譲(Role:Sole author)

    岩波書店  2022.8 

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    Language:Japanese   Book type:Scholarly book

    伊藤流の確率微分方程式論をまったく別の角度から見る「ラフパス理論」は、性質の悪い連続なパスに沿った線積分を、確率論を使わずに定式化することを可能にする。理論の基礎的理解を目指し、ラフパスで駆動される常微分方程式など非測度論的な部分に焦点を当て解説。Brownラフパス理論に関する一連の確率論的な結果についても触れる。

  • ラフパス理論と確率解析

    Inahama Yuzuru

    岩波書店  2022    ISBN:9784000298575

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    Language:Japanese  

    CiNii Books

Presentations

  • Wong-Zakai approximation for density functions Invited International conference

    Yuzuru Inahama

    Oberwolfach workshop 2445 (Directions in Rough Analysis)  Mathematisches Forshungsinstitut Oberwolfach

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    Event date: 2024.11

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Mathematisches Forshungsinstitut Oberwolfach   Country:Germany  

  • Short time full asymptotic expansion of hypoelliptic heat kernel at the cut locus International conference

    稲濱 譲

    Cut Locus -- A Bridge Over Differential Geometry Optimal Control and Transport--  2016.8 

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    Event date: 2016.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:King Monkut's Institute of Technology, Latkrabang, Bangkok, Thailand.   Country:Thailand  

    We prove a short time asymptotic expansion of a hypoelliptic heat kernel on an Euclidean space and a compact manifold.
    We study the "cut locus" case, namely, the case where energy-minimizing paths which join the two points under consideration form not a finite set, but a compact manifold. Under mild assumptions we obtain an asymptotic expansion
    of the heat kernel up to any order. Our approach is probabilistic and the heat kernel is regarded as the density of the law of a hypoelliptic diffusion process, which is realized as a unique solution of the corresponding stochastic differential equation. Our main tools are S. Watanabe's distributional Malliavin calculus and T. Lyons' rough path theory.

MISC

  • ラフパス理論と確率解析

    稲濱 譲

    数学(岩波書店)   2015.7

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    Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (scientific journal)  

Professional Memberships

  • Mathematical Society of Japan

Academic Activities

  • 座長(Chairmanship)

    日本数学会  ( Japan ) 2016.9

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    Type:Competition, symposium, etc. 

Research Projects

  • New developments in stochastic analysis

    Grant number:23K20216  2020.4 - 2025.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    稲浜 譲, 星野 壮登, 村山 拓也

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    Grant type:Scientific research funding

    伊藤清が発明した確率微分方程式をいわば「決定論化」したのが、ラフパス理論である。確率微分方程式と言う確率論の文字通り中心にある。重要な研究対象物を全く違う角度から見る新しい理論である。またラフパス理論の考え方を確率偏微分方程式に適用してできたのが「特異な確率偏微分方程式」理論である。この理論により今まで解けていなかった確率偏微分方程式が系統的に解けるようになった。本研究はこれらの新しくて重要な話題を進展させることを目指す。

    CiNii Research

  • 確率解析の新展開

    Grant number:20H01807  2020 - 2024

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • ラフパス理論とその確率偏微分方程式への応用

    Grant number:EBG5K04922  2015 - 2019

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Authorship:Principal investigator  Grant type:Scientific research funding

Class subject

  • 線形代数学

    2023.4 - 2024.3   Full year

  • 解析学I・演習

    2023.4 - 2023.9   First semester

  • 数理科学特別講義Ⅶ

    2022.4 - 2022.9   First semester

  • ルベーグ積分

    2022.4 - 2022.9   First semester

  • 積分論の基礎

    2022.4 - 2022.9   First semester

  • 数理科学特論7

    2022.4 - 2022.9   First semester

  • 解析学Ⅰ・演習

    2022.4 - 2022.9   First semester

  • Probability

    2021.10 - 2022.3   Second semester

  • 確率論大意

    2021.10 - 2022.3   Second semester

  • 確率論大意

    2021.10 - 2022.3   Second semester

  • 数学特論10(確率論)

    2021.10 - 2022.3   Second semester

  • Probability

    2020.10 - 2021.3   Second semester

  • 線形代数学・同演習B

    2016.10 - 2017.3   Second semester

  • 線形代数学・同演習B

    2016.10 - 2017.3   Second semester

  • 確率論基礎・演習

    2016.10 - 2017.3   Second semester

  • 線形代数学・同演習A

    2016.4 - 2016.9   First semester

  • 線形代数学・同演習A

    2016.4 - 2016.9   First semester

  • 数学展望

    2016.4 - 2016.9   First semester

  • 数学概論IVの演習

    2015.10 - 2016.3   Second semester

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