RESEARCH

Research Interests

Stochastic Processes and Random Fields
Stochastic Partial Differential Equations
Statistical Properties of Gaussian Random Fields
Random Fractal
High Accuracy Finite Element Analysis

 

Dissertation

       Geometric Properties of Anisotropic Gaussian Random Fields. Michigan State University, May 2006. (Thesis Advisor: Professor Yimin Xiao)

Selected Publications and Preprints

  1. Local times of multifractional Brownian sheets. (with Mark Meerschaert and Yimin Xiao). Bernoulli, to appear. (PDF)
  2. Joint continuity of the local times of fractional Brownian sheets. (with Antoine Ayache and Yimin Xiao). Ann. Inst. H. Poincare Prob. Stat., to appear. (PDF)
  3. Dimension results for multifractional Brownian sheets. J. Math. Phy. 48 (2007), Paper 073511. (Journal Link)
  4. Generalized Pickands constants. J. Math. Phy. 48 (2007), Paper 053513. (Journal Link)
  5. Geometric properties of fractional Brownian sheets. (with Yimin Xiao).  J. Fourier Anal. Appl. 13 (2007), 1-37. (PDF)
  6. Dimensional properties of fractional Brownian motion. (with Yimin Xiao).  Acta Math. Sinica. 23 (2007), 613-622. (Journal Link)
  7. Sectorial local nondeterminism and the geometry of the Brownian sheet. (with Davar Khoshnevisan and Yimin Xiao). Electronic J. Probab. 11 (2006), 817-843. (PDF)
  8. Fractal properties of the random string processes. (with Yimin Xiao). IMS Lecture Notes: High Dimensional Probability. 51 (2006), 128-147. (PDF)
  9. Multiple times and joint continuity of self-intersection local times of fractional Brownian sheets. (with Mark Meerschaert and Yimin Xiao). Preprint, 2007.
  10. Continuity with respect to the Hurst index of the local times of anisotropic Gaussian random fields. (with Yimin Xiao) Preprint, 2008.
  11. High accuracy analysis of elliptic eigenvalue problem for the Wilson nonconforming finite element. Acta Math. Appl. Sinica (English Ser.) 17 (2001), 200-206. (Journal Link)
  12. Convergence and superconvergence of Hermite bicubic elements for eigenvalue problem of the biharmonic equation. J. Comput. Math. 19 (2001), 139-142. (Journal Link)
  13. Probabilistic numerical approach for PDE and its application in the valuation of European options. J. Comput. Math. 19 (2001), 591-600. (Journal Link)
  14. High-accuracy approximations for eigenvalue problems by the Carey nonconforming finite element. (with Qun Lin). Comm. Numer. Methods Engrg. 15 (1999), 19-31. (PDF)
  15. The Dirichlet problem of a diffusion equation with vibration boundary values. (with Honglu Wu). (Chinese) J. Math. Res. Exposition, 16 (1996), 213-218.
  16. A probabilistic solution to the Cauchy problem for the convection-diffusion equation. (Chinese) Chinese Sci. Bulletin, 40 (1995), 2209-2211.