Academic Assembly School of Science and Technology (Institute of Science)

Faculty of Science Department of Mathematics Course of Natural Informatics 



  • Ph.D.(Mathematical Science), Japan

Research Keyword

    Probability Theory, Analysis of Probability, Stochastic partial differential equation

Field Of Study

  • Stochastic Analysis
  • Stochastic Partial Differential Equatoin


  • 2021
    Academic Assembly of School of Science and Technology (Institute of Science) (Professor)
  • 2014 - 2021
    Academic Assembly of School of Science and Technology (Institute of Science) (Associate Professor)
  • 2013 - 2014
    Faculty of Science, Shinshu University (Associate Professor)
  • 2010 - 2010
  • 2008 - 2013
    Young Researcher Empowerment Project (Assistant Professor)

Educational Background

  • 2005 - 2008, The University of Tokyo, The Graduate School of Mathematical Sciences, Mathematical Science


  • Log-Harnack inequality for reflected SPDEs driven by multiplicative noises and its applications
    B. Xie
    Stochastics and Partial Differential Equations: Analysis and Computations, 10(2), 419-445, 2022
  • Asymptotics of PDE in random environment by paracontrolled calculus
    T. Funaki, M. Hoshino, S. Sethuraman and B. Xie
    Annales de l'Institut Henri Poincaré-Probabilités et Statistiques, 57(3), 1702-1735, 2021
  • A note on random strings with values in a bounded convex domain
    B. Xie
    RIMS Kôkyûroku Bessatsu, B79(9), 199-213, 2020
  • Ergodicity of stochastic Cahn-Hilliard equations with logarithmic potentials driven by degenerate or nondegenerate noises
    L. Goudenège, B. Xie
    J. Differential Equations, 269(9), 6988-7014, 2020
  • Hypercontractivity for space–time white noise driven SPDEs with reflection
    B. Xie
    J. Differential Equations, 266(9), 5254-5277, 2019
  • Comparison theorem and decorrelation for stochastic heat equation driven by Lévy space-time white noise
    M. Niu, B. Xie
    Discrete & Continuous Dynamical Systems-B, 24(7), 2989-3009, 2019
  • Wang's Harnack inequalities for space-time white noises driven SPDEs with two reflecting walls and their applications
    M. Niu, B. Xie
    J. Math. Anal. Appl. 469, 469(2), 568-593, 2019
  • Intermittency for stochastic partial differential equations driven by strongly inhomogeneous space-time white noises
    B. Xie
    J. Differential Equations, 264(2), 1050-1079, 2018
  • Some effects of the noise intensity upon non-linear stochastic heat equations on [0,1]
    B. Xie
    Stochastic Process. Appl., 126(4), 1184-1205, 2016
  • Fluctuations in an evolutional model of two-dimensional Young diagrams
    T. Funaki, M. Sasada, M. Sauer, B Xie
    Stochastic Process. Appl., 123(2), 1229-1275, 2013
  • Impulsive noise driven 1-dimensional higher order fractional partial differential equations
    B. Xie
    Stochastic Analysis and Applications, 30, 122-145, 2012
  • Uniqueness of Invariant Measures of Infinite Dimensional Stochastic Differential Equations Driven by Levy Noises
    B. Xie
    Potential Analysis, 36(1), 35-66, 2012
  • Impacts of Gaussian noises on the blow-up times of nonlinear stochastic partial differential equations
    M. Niu, B. Xie
    Nonlinear Analysis: Real World Application, 13(3), 1346-1352, 2012
  • On a Burgers type nonlinear equation perturbed by a pure jump Levy noise in
    J-L. Wu, B. Xie
    Bull. Sci. Math., 136(5), 484-506, 2012
  • Regularity of a fractional partial differential equation driven by space-time white noise
    M. Niu, B. Xie
    Proc. Amer. Math. Soc, 138(4), 1479-1489, 2010
  • A stochastic heat equation with the distributions of Lévy processes as its invariant measures.
    T. Funaki, B. Xie
    Stochastic Process. Appl., 119(2), 307-326, 2009
  • The moment and almost surely exponential stability of stochastic heat equations
    B. Xie
    Proc. Amer. Math. Soc., 136, 3627-3634, 2008
  • On pathwise uniqueness of stochastic evolution equations on Hilbert Spaces
    B. Xie
    J. Math. Anal. Appl., 344, 204-216, 2008
  • Stochastic differential equations with non-Lipschitz coefficients in Hilbert spaces
    B. Xie
    Stoch. Anal. Appl., 26, 408-433, 2008

Books and other publications

  • 確率偏微分方程式
    舟木 直久, 乙部 厳己, 謝 賓, Joint work
    岩波書店, 15 Mar. 2019

Affiliated academic society

  • The Mathematical Society of Japan

Research Themes

  • Stochastic analysis on stochastic generalized Cahn-Hilliard equations
    科学研究費補助金, 基盤研究(C)
    2020 - 2023
  • Various properties relative to intermittency of space-time fractional SPDEs
    科学研究費補助金, 基盤研究(C)
    2016 - 2019
  • 分数冪ラプラシアンを持つ確率Burgers方程式の確率解析
    科学研究費補助金, 若手研究(B)
    2013 - 2015
  • 特異性を持つ確率偏微分方程式の研究
    科学研究費補助金, 若手研究(B)
    2009 - 2012
  • 特異性を持つ確率偏微分方程式の研究
    科学研究費補助金, 若手研究(スタートアップ)
    2008 - 2008
  • Stochastic Partial Differential Equations