RESEARCH

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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. Fuzzy aggregation with artificial color filters. (with J. Fu, H.J. Caulfield and S.M. Yoo). Information Sciences. 180 (2010), 167-180. (Journal Link)

2. Regularity of intersection local times of fractional Brownian motions. (with Y. Xiao). J. Theor. Probab. 2009. (Journal Link)

3. Uniform dimension results for Gaussian random fields. (with Y. Xiao). Science in China Series A: Mathematics. 52 (2009), 1478-1496. (Journal Link)

4. Continuity in the Hurst index of the local times of anisotropic Gaussian random fields. (with Y. Xiao). Stoch. Process. Appl., 119 (2009), 1823-1844. (PDF)

5. Local times of multifractional Brownian sheets. (with M. Meerschaert and Y. Xiao). Bernoulli, 14 (2008), 865-898. (PDF)

6. Joint continuity of the local times of fractional Brownian sheets. (with A. Ayache and Y. Xiao). Ann. Inst. H. Poincare Prob. Stat., 44 (2008),  727-748. (PDF)

7. Capacity analysis of an ultrawideband active RFID system. (with F. Kheiri, B. Dewberry and L. Joiner). Proc. IEEE SoutheastCon 2008, Huntsville, Alabama, April 2008.

8. Dimension results for multifractional Brownian sheets. J. Math. Phy. 48 (2007), Paper 073511. (Journal Link)

9. Generalized Pickands constants. J. Math. Phy. 48 (2007), Paper 053513. (Journal Link)

10. Geometric properties of fractional Brownian sheets. (with Y. Xiao). J. Fourier Anal. Appl. 13 (2007), 1-37. (PDF)

11. Dimensional properties of fractional Brownian motion. (with Y. Xiao).  Acta Math. Sinica. 23 (2007), 613-622. (Journal Link)

12. Sectorial local nondeterminism and the geometry of the Brownian sheet. (with D. Khoshnevisan and Y. Xiao). Electronic J. Probab. 11 (2006), 817-843. (PDF)

13. Fractal properties of the random string processes. (with Y. Xiao). IMS Lecture Notes: High Dimensional Probability. 51 (2006), 128-147. (PDF)

14. 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)

15. Convergence and superconvergence of Hermite bicubic elements for eigenvalue problem of the biharmonic equation. J. Comput. Math. 19 (2001), 139-142. (Journal Link)

16. Probabilistic numerical approach for PDE and its application in the valuation of European options. J. Comput. Math. 19 (2001), 591-600. (Journal Link)

17. High-accuracy approximations for eigenvalue problems by the Carey nonconforming finite element. (with Q. Lin). Comm. Numer. Methods Engrg. 15 (1999), 19-31. (PDF)

18. The Dirichlet problem of a diffusion equation with vibration boundary values. (with H. Wu). (Chinese) J. Math. Res. Exposition, 16 (1996), 213-218.

19. A probabilistic solution to the Cauchy problem for the convection-diffusion equation. (Chinese) Chinese Sci. Bulletin, 40 (1995), 2209-2211.

20. Hyperspectral image analysis using artificial color. (with J. Fu, H.J. Caulfield and W. Tadesse). Submitted, 2008.

21. Multiple times and joint continuity of self-intersection local times of fractional Brownian sheets. (with M. Meerschaert and Y. Xiao). Preprint, 2007.

Conferences

• The Third International Conference on Stochastic Analysis and Its Applications, Beijing Institute of Technology, Beijing, China, July 13--17, 2009.
• IMS-China International Conference on Statistics and Probability 2009, Shandong University, Weihai, China, July 3--6, 2009. 
• The First IMS Asia Pacific Rim Meeting, Seoul National University, Seoul, Korea, June 28--July 1, 2009.
• Spring School on Random Differential Equations and Gaussian Fields, Chateau de Mons, France, June 15--19, 2009.
• 2009 Barrett Lectures at The University of Tennessee, Knoxville, April 17--18, 2009.
• Workshop on "Small Ball Inequalities in Analysis, Probability, and Irregularities of Distribution", American Institute of Mathematics, Dec. 8--12, 2008.
• The Seventh Northeast Probability Seminar, New York University, Nov. 20--21, 2008.
• Special Session on "Gaussian Analysis & Stochastic Partial Differential Equations" at AMS 2008 Fall Southeastern Meeting, The University of Alabama in Huntsville, Oct. 24--26, 2008.
• CBMS Research Conference on Malliavin Calculus and its Applications, Kent State University, Aug. 7--12, 2008.
• IMS-China International Conference on Statistics and Probability 2008, Zhejiang University, Hangzhou, China, June 11--13, 2008.
• Seminar on Stochastic Processes 2008, University of Delaware, April 3--5, 2008.