Meeting Young Researchers



Research Area:
Stochastic analysis
Stochastic differential equation, stochastic partial differential equation, Ito's Analysis, large deviation principle, probability inequality, fluctuation, interacting system

Employment Experience:
April 2008 – :
Tenure-Track Assistant Professor, Young Researcher Empowerment Project, Shinshu University

Oct. 2004 – Mar. 2004:
Researcher, Graduate School of Mathematical Sciences,the University of Tokyo

Apr. 2004 – Mar. 2005:
Master, Graduate School of Mathematical Sciences, the University of Tokyo

Apr. 2005 – Mar. 2008:
Doctor, Graduate School of Mathematical Sciences, the University of Tokyo

Oct. 2003 – Mar. 2008:
Japanese Government Scholarship

Mar. 2008:
Award from the dean of the Graduate School of Mathematical Sciences, the University of Tokyo

Selected Publications:
  • B. Xie, The growth estimates for direction dependent random fields. Far East J. Math. Sci. (FJMS) 44 (2010), no. 2, 181-195.
  • M. Niu and B. Xie, Regularity of a fractional partial differential equation driven by space-time white noise. Proc. Amer. Math. Soc. 138 (2010), no. 4, 1479-1489.
  • T. Funaki and B. Xie, A stochastic heat equation with the distributions of Lévy processes as its invariant measures. Stochastic Process. Appl. 119 (2009), no. 2, 307-326.
  • B. Xie, The moment and almost surely exponential stability of stochastic heat equations, Proc. Amer. Math. Soc. 136 (2008), 3627-3634.
  • B. Xie, On pathwise uniqueness of stochastic evolution equations on Hilbert Spaces. J. Math. Anal. Appl. 339 (2008) 705-718.
  • B. Xie, Stochastic differential equations with non-Lipschitz coefficients in Hilbert spaces. Stochastic Analysis and Applications, 26: 408-433, 2008
  • B. Xie, The stochastic parabolic partial differential equation with non-Lipschitz coefficients on the unbounded domain. J. Math. Anal. Appl. 344 (2008) 204-216.
  • L. Lei, L. Wu and B. Xie, Large Deviations and Deviation Inequality for Kernel Density Estimator in L1(Rd) -distance. Development of Modern Statistics and Related Topics , Ser. Biostat. 1. (2003), 89-97, World Sci. Publishing, River Edge, NJ.
  • B. Xie, Hypercontractivity of Hamilton-Jacobi equations and related inequalities. J. Math. (Wuhan) 23 (2003), no. 4, 397--402.

Research Statement

I am mainly interested in stochastic analysis, especially, in infinite dimensional stochastic differential equations driven by several different noises, like white noise and Levy type noise. Infinite dimensional stochastic differential equations are, roughly speaking, infinite dimensional deterministic differential equations containing some random terms, which are motivated by internal development of analysis and theory of stochastic processes on one side, and by applications to describing the random phenomena studied in natural sciences on the other hand. Such equations are key ingredients of mathematical modeling in numerous fields like population genetics, quantum fields, statistical physics, neurophysiology and oceanography. In fact, all kinds of dynamics with stochastic influence in nature or man-made complex systems can be described by such equations. I mainly investigated stochastic heat equations, stochastic wave equations and stochastic Burgers equations driven by continuous and discontinuous noises in the past.