Updated on 2024/04/18

写真a

 
LIANG, Song
 
Affiliation
Faculty of Education and Integrated Arts and Sciences, School of Education
Job title
Professor
Degree
博士(数理科学) ( 東京大学 )

Research Experience

  • 2008.04
    -
     

    University of Tsukuba

  • 2004.04
    -
    2008.03

    Tohoku University   Graduate School of Information Sciences

  • 2005
     
     

    ボン大学

  • 2000.04
    -
    2004.04

    Nagoya University   Graduate School of Mathematics

  • 2003
    -
    2004

    ボン大学

  • 2001
    -
    2002

    ボン大学

  •  
     
     

    University of Tsukuba Faculty of Pure and Applied Sciences   Associate Professor

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Papers

  • A Mechanical Model of Brownian Motion for One Massive Particle Including Slow Light Particles

    Song Liang

    Journal of Statistical Physics   170 ( 2 ) 286 - 350  2018.01  [Refereed]

     View Summary

    We provide a connection between Brownian motion and a classical mechanical system. Precisely, we consider a system of one massive particle interacting with an ideal gas, evolved according to non-random mechanical principles, via interaction potentials, without any assumption requiring that the initial velocities of the environmental particles should be restricted to be “fast enough”. We prove the convergence of the (position, velocity)-process of the massive particle under a certain scaling limit, such that the mass of the environmental particles converges to 0 while the density and the velocities of them go to infinity, and give the precise expression of the limiting process, a diffusion process.

    DOI

    Scopus

    1
    Citation
    (Scopus)
  • A Classical Mechanical Model of Brownian Motion with One Particle Coupled to a Random Wave Field

    Shigeo Kusuoka, Song Liang

    STOCHASTIC ANALYSIS AND APPLICATIONS   30 ( 3 ) 493 - 528  2012  [Refereed]

     View Summary

    We consider the problem of deriving Brownian motions from classical mechanical systems. Specifically, we consider a system with one massive particle coupling to an ideal random wave field, evolved according to classical mechanical principles. We prove the almost sure existence and uniqueness of the solution of the considered dynamics, prove the convergence of the solution under a certain scaling limit and give the precise expression of the limiting process, a diffusion process.

    DOI

    Scopus

  • A CLASSICAL MECHANICAL MODEL OF BROWNIAN MOTION WITH PLURAL PARTICLES

    Shigeo Kusuoka, Song Liang

    REVIEWS IN MATHEMATICAL PHYSICS   22 ( 7 ) 733 - 838  2010.08  [Refereed]

     View Summary

    We give a connection between diffusion processes and classical mechanical systems in this paper. Precisely, we consider a system of plural massive particles interacting with an ideal gas, evolved according to classical mechanical principles, via interaction potentials. We prove the almost sure existence and uniqueness of the solution of the considered dynamics, prove the convergence of the solution under a certain scaling limit, and give the precise expression of the limiting process, a diffusion process.

    DOI

    Scopus

    12
    Citation
    (Scopus)
  • A formula to compute implied volatility, with error estimate

    Liang, Song, Tahara, Yoshihiro

    Interdisciplinary information sciences   15 ( 2 ) 267 - 272  2009.08  [Refereed]

     View Summary

    We derive a simple formula to compute implied volatility approximately, and give an estimate of its relative error, in the framework developed by Black-Scholes. In particular, our error estimate ensures that the relative error of our formula is converging to 0 under certain condition.

    DOI CiNii

  • A remark on the nonequivalence of the time-zero $ \phi_3^4 $-measure with the free field measure

    S., Albeverio, S., Liang

    Markov Processes and Related Fields   14 ( 1 ) 159--164  2008.01  [Refereed]

  • A mechanical model of Markov processes

    S., Kusuoka, S., Liang

    RIMS Kokyuuroku   Bessatsu B6   167--176  2008.01  [Refereed]

  • Laplace approximations for large deviations of diffusion processes on Euclidean spaces

    S Liang

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   57 ( 2 ) 557 - 592  2005.04  [Refereed]

     View Summary

    Consider a class of uniformly elliptic diffusion processes {X-t}t >= 0 on Euclidean spaces R-d. We give an estimate of E-Px [exp(T Phi(1/T integral(T)(O) delta(Xt)dt))vertical bar X-T =y] as T -> infinity up to the order 1 + o(1), where delta. means the delta measure, and Phi is a function on the set of measures on R-d. This is a generalization of the works by Bolthausen-Deuschel-Tamura [3] and Kusuoka-Liang [10], which studied the same problems for processes on compact state spaces.

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Presentations

  • A classical mechanical model of Diffusion process -- with existence of low energy light particles

    梁,松

    symposium on probability theory  (Japan Sendai) 

    Presentation date: 2017.12

  • Diffusion and classical dynamics

    Liang,Song  [Invited]

    Mathematical Aspects of Quantum Fields and Related Topics  (Kyoto) 

    Presentation date: 2017.06

Research Projects

  • 結晶確率モデルのハミルトン力学系による導出およびそれにおける相対効果の影響

    日本学術振興会  若手研究(B)

    Project Year :

    2013.04
    -
    2017.03
     

    梁松

  • 結晶確率モデルのハミルトン力学系による導出及びそれにおける相対効果の影響

    日本学術振興会  若手研究(B)

    Project Year :

    2013
    -
    2016
     

    梁 松

  • 結晶確率モデルの古典力学系による導出

    日本学術振興会  若手研究(B)

    Project Year :

    2009
    -
    2012
     

    梁松

  • 拡散過程の古典力学系による導出

    日本学術振興会  若手研究(B)

    Project Year :

    2006
    -
    2008
     

    梁松

 

Syllabus

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Sub-affiliation

  • Faculty of Education and Integrated Arts and Sciences   Graduate School of Education