Yimin Xiao
                                                                                        
Professor
                                                                                Department of Statistics and Probability
                                                                                             Michigan State University

 

                                                                                                         Contact Information
                                                                                                         
E-mail: xiao@stt.msu.edu
                                                                                                                                              Phone:  (517) 432-5411
                                                                                                                                              Fax:        (517) 432-1405


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During 2007--2008, I will be visiting
Statistical and Applied Mathematical Sciences Institute.



Colloquiua of Department of Statistics and Probability



Research Interests

Stochastic processes and random fields: Gaussian and stable random fields, self-similar processes, L¨¦vy processes, additive L¨¦vy processes and the L¨¦vy sheets.


Fractal geometry: Measure theory of random fractals, Hausdorff and packing dimensions.


Nonparametric regression: Long memory (long range dependence), wavelet methods.

 

Survey Articles

 

[3]. Properties of local nondeterminism of Gaussian and stable random fields and their applications.  Ann. Fac. Sci. Toulouse Math. XV (2006), 157¡ª193.

 

[2]. Additive L¨¦vy processes: capacity and Hausdorff dimension. (with Davar Khoshnevisan)  Proc. of Inter. Conf. on

Fractal Geometry and Stochastics III., Progress in Probability, 57, pp. 151--170, Birkhauser, 2004.

 

[1]. Random fractals and Markov processes. In: Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot,

(Michel L. Lapidus and Machiel van Frankenhuijsen, editors), pp. 261--338, American Mathematical Society, 2004.



Preprints and Selected Recent Publications



[27]. Properties of strong local nondeterminism and local times of stable random fields. Submitted, 2008.

[26]. A packing dimension theorem for Gaussian random fields. Submitted, 2008.

[25]. Continuity with respect to the Hurst index of the local times of anisotropic Gaussian random fields.. (with D. Wu). Submitted, 2008.

[24]. Hitting probabilities and the Hausdorff dimension of the inverse images of anisotropic Gaussian random fields. (with H. Bierme and C. Lacaux ). Submitted, 2008.

[23]. Large deviations for local time fractional Brownian motion and applications. (with M. M. Meerschaert and E. Nane). Submitted, 2007.

[22]. Linear fractional stable sheets: wavelet expansion and sample path properties. (with A. Ayache and F. Roueff). Submitted, 2007.

[21]. On block thresholding in wavelet regression with long memory correlated noise. (with Linyuan Li). Submitted, 2007.

[20]. Harmonic analysis of additive Levy processes. (with D. Khoshnevisan). Submitted, 2007.

[19]. Sample path properties of anisotropic Gaussian random fields. Submitted, 2007.

[18]. Local times of multifractional Brownian sheets. (with M. Meerschaert and D. Wu). To appear in Bernoulli.

[17]. Packing dimension profiles and fractional Brownian motion. (with D. Khoshnevisan). To appear in Math. Proc.
Cambridge Philo. Soc.


[16]. Packing dimension of the range of a Levy process. (with D. Khoshnevisan). To appear in Proc. Amer. Math. Soc.

[15]. Joint continuity of the local times of fractional Brownian sheets. (with Antoine Ayache and D. Wu). To appear in Ann.
Inst. H. Poincare Probab. Statist.
.

[14]. Hausdorff dimension of the contours of symmetric additive Levy processes. (with D. Khoshnevisan and N.-R. Shieh). Probab. Th. Rel. Fields. 140, 169--193. [The original publication is available at www.springerlink.com.]

[13]. Sample path properties of bifractional Brownian motion. (with Ciprian A. Tudor). Bernoulli 14 (2007), 1023--1052.

[12]. Joint continuity of the local times of linear fractional stable sheets. (with A. Ayache and F. Roueff). C. R. Acad. Sci.
Paris, Ser. A.
344 (2007), 635--640.

[11]. Local and asymptotic properties of linear fractional stable sheets. (with A. Ayache and F. Roueff). C. R. Acad. Sci.
Paris, Ser. A.
344 (2007), 389--394.

[10]. On the minimax optimality of block thresholded wavelet estimators with long memory data. (with Linyuan Li) J. Statist. Plann. Inference 137 (2007), 2850--2869.

[9]. Mean integrated squared error of nonlinear wavelet-based estimators with long memory data. (with Linyuan Li) Ann. Inst. Statist. Math. 59 (2007), 299--324.

[8]. Geometric properties of the images fractional Brownian sheets (with D. Wu). J. Fourier Anal. Appl. 13 (2007), 1--37. [The original publication is available at www.springerlink.com .]

[7]. Images of the Brownian sheet. (with Davar Khoshnevisan)   Trans. Amer. Math. Soc. 359 (2007), 3125--3151.

[6]. Sectorial local non-determinism and the geometry of the Brownian sheet
(with D. Khoshnevisan and D. Wu). Electron. J. Probab. 11 (2006), 817--843.

[5]. Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets. (with Antoine Ayache) J. Fourier Anal. Appl. 11 (2005), 407--439. [The original publication is available at www.springerlink.com.]

[4]. L¨¦vy processes: capacity and Hausdorff dimension. (with Davar Khoshnevisan) Ann. Probab. 33 (2005), 841--878.

[3]. Packing measure of the trajectories of multiparameter fractional Brownian motion. Math. Proc. Cambridge Philo. Soc. 135 (2003), 349--375

[2]. Measuring the range of an additive L¨¦vy process. (with Davar Khoshnevisan and Yuquan Zhong) Ann. Probab. 31 (2003), 1097--1141.

[1]. Level sets of additive Levy process. (with Davar Khoshnevisan) Ann. Probab. 30 (2002), 62--100.


More Publications  Click here

Some Talks


[1]. Packing Dimension Profiles and Random Fractals. for Mini-Symposium on Geometry of Random Fractals. Berlin, Germany, March 25--30, 2007.

[2]. Sample Path Properties of Anisotropic Gaussian Random Fields. Probability Seminar at the University of Utah, February 22, 2006.

[3]. Properties of Local Nondeterminism of Self-Similar Random Fields and Their Applications. (Second Conference on Self-Similarity and Applications at L¡¯Institut National des Sciences Appliqu¨¦s, Toulouse, France, June 20--24, 2005).

[4]. Potential Theory of Additive Levy Processes, Capacity and Hausdorff Dimension. (The First Northeastern Probability Seminar at CUNY's Graduate Center on November 20--21, 2003).

[5]. Fractal Geometry of Random Fields. (International Conference on Fractal Geometry & Stochastics III at Friedrichroda, Germany, March 17--22, 2003).


Some Related Conferences

 


[26]. The first IMS-China International Conference on Statistics and Probability. Hangzhou, June 11--13, 2008.

[25]. The 2nd International Conference on Stochastic Analysis and Its Applications (ICSAA). Seoul National University, Seoul, Korea, May 28--31, 2008.

[24]. The Fifth International Conference on High Dimensional Probability. The Centre International de Recntres Mathematiques (C.I.R.M.) in Luminy, France, May 26-May 30, 2008.

[23]. Stochastic Analysis, Random Fields and Applications. Ascona, Switzerland, May 19--23, 2008.

[22]. Seminar on Stochastic Processes. University of Delaware, April 3--5, 2008.

[21]. Fractals and Related Fields. Monastir, Tunisia, September 8--13, 2007.

[20]. Levy Processes: Theory and Applications. Copenhagen, Denmark, August, 13--17, 2007.

[19]. 32nd Conference on Stochastic Processes and Their Applications. University of Illinois at Urbana-Champaign, August, 6--10, 2007.

[18]. Mini-Workshop on "Geometric Measure Theoretic Approaches to Potentials on Fractals and Manifolds". Oberwolfach Research Institute (MFO), Germany. April 8--14, 2007.

[17]. Mini-Symposium on Geometry of Random Fractals. Berlin, Germany, March 25--30, 2007.

 

[16]. Twenty Eighth Midwest Probability Colloquium at the Northwestern University, October 21--22, 2006.

 

[15]. Interface of Stochastic PDEs and Gaussian Analysis at the University of Utah, October 7-- 8, 2006.

 
[14]. Mathematics on Fractals 2006 at Kyoto University, Japan, September 4--8, 2006.

 

[13]. The 31st  Conference on Stochastic Processes and Their Applications. Paris, July 17¡ª21, 2006.

 

[12]. International Conference on Asymptotic Theory in Probability and Statistics. CMS, Zhejiang University, June 18¡ª21, 2006.

[11]. Minicourse on Stochastic Partial Differential Equations. Organized by Davar Khoshnevisan at the University of Utah, May 8 ¨C19, 2006.

[10]. Workshop on Stochastic and Harmonic Analysis of Processes with Jumps. Angers, France, May 2¡ª9, 2006.

 

[9]. Special Session on Fractal Geometry: Connections to Dynamics, Geometric Measure Theory, Mathematical Physics and Number Theory. AMS Spring Western Section Meeting, San Francisco, CA, April 29--30, 2006.

 

[8]. Seminar on Stochastic Processes 2006. Princeton University, Princeton, New Jersey,  March 23--25, 2006.

 

[7]. The Fourth Northeastern Probability Seminar at CUNY's Graduate Center, November 17--18, 2005.   

[6]. Workshop on Small Deviation Problems for Stochastic Processes and Related Topics, in St.Petersburg, Russia,   September 12¡ª19, 2005.

[5]. Second Conference on Self-Similarity and Applications at L¡¯Institut National des Sciences Appliqu¨¦s, Toulouse, France, from Monday, June 20--24, 2005.

[4]. The Fourth International Conference on High Dimensional Probability (HDP) . Santa Fe, New Mexico, June 20--24, 2005.

[3]. Fourth Symposium on Levy Processes: Theory and Applications Manchester University, England, January 10--15, 2005.

[2]. The Third International Congress of Chinese Mathematicians in Hong Kong,  December 17--22, 2004.

[1]. Power Laws in Probability and Statistics, Centre International de Rencontres Mathematiques, France , March 22--26, 2004.


Created by:Yimin Xiao
Last Modified: 03/20/2007.

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Created by:Yimin Xiao
Last Modified: 03/20/2007.