Details of the Researcher

PHOTO

Yu Hariya
Section
Graduate School of Science
Job title
Professor
Degree

  • 博士（数理科学） (The University of Tokyo)

Professional Memberships 1

  • Mathematical Society of Japan

Research Interests 1

  • 確率論

Research Areas 2

  • Natural sciences / Applied mathematics and statistics /

  • Natural sciences / Basic mathematics /

Papers 13

  1. On divergence of expectations of the Feynman-Kac type with singular potentials Peer-reviewed

    Yuu Hariya, Kaname Hasegawa

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN　68　(3)　1271-1296　2016/07

    DOI： 10.2969/jmsj/06831271 　

    ISSN： 0025-5645

  2. On an extension of the Brascamp-Lieb inequality Invited Peer-reviewed

    Yuu Hariya

    RIMS Kokyuroku Bessatsu　B59　85-100　2016/07

  3. A pathwise interpretation of the Gorin-Shkolnikov identity Peer-reviewed

    Yuu Hariya

    ELECTRONIC COMMUNICATIONS IN PROBABILITY　21　(52)　1-6　2016

    DOI： 10.1214/16-ECP10 　

    ISSN： 1083-589X

  4. Some Asymptotic Formulae for Bessel Process Peer-reviewed

    Y. Hariya

    MARKOV PROCESSES AND RELATED FIELDS　21　(2)　293-316　2015

    ISSN： 1024-2953

  5. A connection of the Brascamp-Lieb inequality with Skorokhod embedding Peer-reviewed

    Yuu Hariya

    ELECTRONIC COMMUNICATIONS IN PROBABILITY　19　(61)　1-12　2014/08

    DOI： 10.1214/ECP.v19-3025 　

    ISSN： 1083-589X

  6. STOCHASTIC RANKING PROCESS WITH TIME DEPENDENT INTENSITIES Peer-reviewed

    Yuu Hariya, Kumiko Hattori, Tetsuya Hattori, Yukio Nagahata, Yuusuke Takeshima, Takahisa Kobayashi

    TOHOKU MATHEMATICAL JOURNAL　63　(1)　77-111　2011/03

    DOI： 10.2748/tmj/1303219937 　

    ISSN： 0040-8735

  7. Wiener integrals for centered powers of Bessel processes. I Invited Peer-reviewed

    Tadahisa Funaki, Yuu Hariya, Marc Yor

    Markov Processes and Related Fields　13　(1)　21-56　2007/04

  8. On some Fourier aspects of the construction of certain Wiener integrals Peer-reviewed

    T. Funaki, Y. Hariya, F. Hirsch, M. Yor

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS　117　(1)　1-22　2007/01

    DOI： 10.1016/j.spa.2006.06.002 　

    ISSN： 0304-4149

    eISSN： 1879-209X

  9. On the construction of Wiener integrals with respect to certain pseudo-Bessel processes Peer-reviewed

    T. Funaki, Y. Hariya, F. Hirsch, M. Yor

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS　116　(12)　1690-1711　2006/12

    DOI： 10.1016/j.spa.2006.05.001 　

    ISSN： 0304-4149

  10. Integration by parts formulae for Wiener measures restricted to subsets in R-d Peer-reviewed

    Yuu Hariya

    JOURNAL OF FUNCTIONAL ANALYSIS　239　(2)　594-610　2006/10

    DOI： 10.1016/j.jfa.2006.06.011 　

    ISSN： 0022-1236

  11. Wiener integrals for centered Bessel and related processes. II Invited Peer-reviewed

    Tadahisa Funaki, Yuu Hariya, Marc Yor

    ALEA. Latin American Journal of Probability and Mathematical Statistics　1　225-240　2006

  12. A time-change approach to Kotani's extension of Yor's formula Peer-reviewed

    Yuu Hariya

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN　58　(1)　129-151　2006/01

    DOI： 10.2969/jmsj/1145287096 　

    ISSN： 0025-5645

  13. On an extension of Dufresne's relation between exponential Brownian functionals from opposite drifts to two different drifts: A short proof Peer-reviewed

    Yuu Hariya, Marc Yor

    Statistics and Probability Letters　67　(4)　331-341　2004/05/01

    DOI： 10.1016/j.spl.2004.02.005 　

    ISSN： 0167-7152

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Misc. 2

  1. Diffusion processes on path spaces with interactions

    Y Hariya, H Osada

    REVIEWS IN MATHEMATICAL PHYSICS　13　(2)　199-220　2001/02

    DOI： 10.1142/S0129055X01000661 　

    ISSN： 0129-055X

  2. Diffusion processes on path spaces with interactions

    Reviews in Mathematical Physics　Vol.13 pp.199-220　2001

    DOI： 10.1142/S0129055X01000661 　

Presentations 8

  1. Ornstein-Uhlenbeck 半群の超縮小性とその指数関数型とを結ぶ 不等式 Invited

    針谷 祐

    確率解析の諸相　2018/01/06

  2. A unifcation of the hypercontractivity and its exponential variant of the Ornstein-Uhlenbeck semigroup International-presentation Invited

    HARIYA Yuu

    16th Stochastic Analysis on Large Scale Interacting Systems　2017/11/09

  3. A pathwise interpretation of the Gorin-Shkolnikov identity

    日本数学会秋季総合分科会　2016/09/15

  4. On an application of Skorokhod embedding International-presentation

    Brownian Motion and Stochastic Processes　2016/06/03

  5. 特異ポテンシャルをもつFeynman-Kac型期待値の発散について

    偏微分方程式に付随する確率論的問題　2014/09/16

  6. A connection of the Brascamp-Lieb inequality with Skorokhod embedding

    新潟確率論ワークショップ　2013/12/05

  7. A time-change approach to Kotani's extension of Yor's formula International-presentation

    Probability Theory and Related Topics-Oidemase Yamaguchi Symposium　2006/11/13

  8. Construction of Gibbs measures for 1-dimensional continuum fields International-presentation

    厳密統計力学と数学的場の量子論の現在（Current Status of Rigorous Statistical Mechanics）　2006/09/04

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Research Projects 11

  1. マルコフ半群の超縮小性と関連する関数不等式の確率解析

    針谷 祐

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 基盤研究(C)

    Institution: 東北大学

    2022/04/01 - 2026/03/31

  2. Study of Skorokhod embeddings and associated variational inequalities

    Hariya Yuu

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Tohoku University

    2017/04/01 - 2022/03/31

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    The Ornstein-Uhlenbeck semigroup defined in a Gaussian space is known to possess the hypercontractivity, which property has applications in mathematical physics such as quantum field theory. As one of the achievements of our study, we have applied stochastic analysis to obtain a family of functional inequalities that embraces the above-mentioned hypercontractivity. As for Brownian motion itself on which stochastic analysis is developed, we have revealed some invariance of the law of Brownian motion under a transformation involving its exponential functionals, which is new to our best knowledge, and which we think is of significance in probability theory because of its fundamental feature of Brownian motion.

  3. Stochastic Analysis on infinite dimensional spaces

    Aida Shigeki, Shigekawa Ichiro, Hino Masanori, Kawabi Hiroshi, Inahama Yuzuru, Hiroshima Fumio, Kuwada Kazumasa, Hariya Yuu

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2012/04/01 - 2016/03/31

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    We studied the spectral property of OU operators on infinite dimensional spaces. This is an infinite dimensional version of the study of semiclassical behaviour of the spectral gap of the operator. We determined the asymptotic behaviour of the spectral gap of the OU operator on a loop space of the rotationally symmetric Riemannianmanifold by the hessian of the energy function at the geodesic. Also we studied stochastic differential equations and rough differential equations. We proved that the Wong-Zakai approximation solution of the reflected stochastic differential equation converges to the solution and formulated reflected rough differential equations and proved the existence of the solutions.

  4. Probabilistic derivation of asymptotic estimates of heat kernels and study of convex inequalities

    HARIYA Yuu

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Young Scientists (B)

    Institution: Tohoku University

    2012/04/01 - 2015/03/31

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    1. The Brascamp-Lieb inequality has importance in statistical mechanics, such as in the analysis of interface models. We give a simple proof of the inequality based on stochastic analysis; as an application of our method, also derived are error estimates of the inequality and its extensions to nonconvex potentials. 2. We recover the principle terms in asymptotic estimates for tail probabilities of first hitting times of Bessel process in a relatively simple manner based on the weak convergence of probability measures; sharp asymptotics of remainder terms are also derived. 3. We clarify sufficient conditions for expectations of the Feynman-Kac type with singular potentials to diverge in the following three cases: Brownian motion, symmetric stable process, and Brownian motion in the half-space with singular potentials on the boundary.

  5. Basic research for renormalization group oriented stochastic analysis

    HATTORI Tetsuya, MINAMI Nariyuki, YASUDA Kumi, ATSUJI Jun, HATTORI Kumiko, TAKEDA Masayoshi, SUZUKI Yuki, HARIYA Yuu

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Keio University

    2009/04/01 - 2014/03/31

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    We defined a class of stochastic ranking models, which mathematically models the rankings found on the web, e.g., as sales ranks of online bookstores, and proved existence of hydrodynamic limits and propagation of chaos. The result has implications on the analysis of so called long-tail structure of online retails. The results are reported in the book `Solving the mystery of Amazon ranking' (in Japanese), as well as in scientific papers for journals on mathematics.

  6. New development of infinite dimensional stochastic analysis and its applications

    AIDA Shigeki, SHIGEKAWA Ichiro, MATSUMOTO Hiroyuki, HANDA Kenji, KAWABI Hiroshi, INAHAMA Yuzuru, NAGAHATA Yukio, YANO Kouji, HINO Masanori, KOHATSU-HIGA Arturo, HIROSHIMA Fumio, TANIGUCHI Setsuo, HARIYA Yuu, NINOMIYA Shoiti, TAKANOBU Satoshi, OHTA Shin-ichi, MIKAMI Toshio

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (A)

    2009 - 2011

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    The study subjects and results are as follows: (1) Laplace approximation and the vanishing of L^2-cohomologies of loop groups from the view point of rough path analysis, (2) Studies on semi-classical properties of Hamiltonian in quantum field theory, Studies from the view point of functional integration, (3)Basic results on the geometry of the space of probability measures (4)Basic study on Sobolev spaces on H-convex set in Wiener spaces and penalization problem and basic results for probability theory

  7. Development of infinite-dimensional stochastic analysis forapplications to non-Markovian fields

    HARIYA Yuu

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Young Scientists (B)

    Institution: Tohoku University

    2007 - 2009

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    (1) I have found a path decomposition of multi-dimensional Brownian motion that relates a type of divergence formula on Wiener space obtained by myself, and Hadamard's variational formula for heat kernels of parabolic equations with Dirichlet boundary conditions. (2) Concerning long-time asymptotics of heat kernels for parabolic equations, I have given a probabilistic explanation by means of a time-change argument which I developed in 2006, in the case where the dimension is one and associated potentials satisfy a certain integrability condition.

  8. Towards a mathematical foundation of renormalization group oriented stochastic analysis

    HATTORI Tetsuya, TAKEDA Masayoshi, NAKANISHI Toshihiro, NAWA Hayato, HATTORI Kumiko, LIANG Song, HARIYA Yuu

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2005 - 2008

  9. ブラウン運動の相互作用を持つ汎関数の研究と対応する無限次元拡散過程の構成及び解析

    針谷 祐

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 特別研究員奨励費

    Institution: 東北大学

    2006 - 2006

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    舟木直久氏(東大数理),F. Hirsch氏(Evry),M. Yor氏(ParisVI)との共同研究で,Bessel過程及びそれを含む広いクラスの確率過程に対するWiener型積分の定義可能性についての研究を行った.いま特にBessel過程を原点から出発させよう.その半マルチンゲール分解には原点での特異性が現れるため,Wiener積分を定義するためには試験関数が2乗可積分という条件だけでは不十分である(これは例えばJeulin's conditionとして知られる条件からも覗える).舟木,Yor両氏との先行する共同研究"Wiener integrals for centered powers of Bessel processes, I", Markov Processes and Related Fieldsに掲載決定)において我々は,原点から出発するBessel過程そのものについては試験関数が2乗可積分というだけではWiener積分を必ずしも定義出来ないが,平均値を引いた中心化過程については全ての2乗可積分な試験関数についてWiener積分が定義出来ることを確かめた.これは,中心化の操作により原点での特異性が除去された結果であると考えられるものの,そこで用いた方法は具体的計算に依っており,何故中心化を考えることでその様な現象が生じたのかというところまで理解出来たとは言えなかった.その現象のより深い理解を得るべく,擬Bessel過程と我々が呼ぶ,中心化Bessel過程を含むより広いクラスの確率過程の族を導入し,対象とする確率過程の分散とFourier解析に現れる正値関数との間の関係等を明らかにした.

  10. パス空間上のギブス測度に関する研究 Competitive

    2000 - 2004

  11. Study of Gibbs Measures on Path Spaces Competitive

    2000 - 2004

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Social Activities 1

  1. 第22回 高校生のための仙台数学セミナー

    2015/08/17 -

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    高校生向け講演「確率を応用してゲームを最適にやめるには」