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Teaching (Fall Semester, 2009)
STT 881:
M. W. F. 1:50--2:40pm; C-102 Wells Hall
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
[30]. Hausdorff and packing dimensions of the images
of random fields. (with N.-R. Shieh),
Submitted, 2009.
[29]. Properties of strong local nondeterminism and local
times of stable random fields.
Submitted, 2008.
[28]. Regularity of intersection local times of
fractional Brownian motions.
(with D. Wu).
To appear in J. Theoret. Probab. 2009.
[27].
On uniform modulus of continuity of random fields. To appear in
Monatsh. Math., 2009.
[26].
Correlated continuous time random walks. (with
M. M. Meerschaert and E. Nane).
Statist.
Probab. Letters 79 (2009), 1194--1202.
[25].
Continuity with respect to the Hurst index
of the local times of anisotropic Gaussian
random fields.
(with D. Wu).
Stochastic Process. Appl. 119 (2009),
1823--1844
[24].
Hitting probabilities and the Hausdorff dimension of the
inverse images of anisotropic
Gaussian random fields.
(with H. Bierme
and C. Lacaux ).
Bull. London Math. Soc. 41 (2009), 253--273
[23].
A packing dimension theorem for Gaussian random fields.
Statist. Probab. Letters 79 (2009), 88--97.
[22].
Harmonic analysis of additive Levy
processes. (with D.
Khoshnevisan). Probab. Theory
Rel. Fields, 2008.
[The original
publication is available at
http://www.springerlink.com]
[21]. Sample
path properties of anisotropic Gaussian random fields.
In: A Minicourse on Stochastic
Partial
Differential Equations, (D. Khoshnevisan and F. Rassoul-Agha, editors),
Lecture Notes
in Math. 1962, pp. 145--212,
Springer, New York, 2009.
[20].
Linear fractional stable sheets: wavelet
expansion and sample path properties. (with A. Ayache
and F. Roueff).
Stochastic Process. Appl. 119 (2009), 1168–-1197.
[19].
Packing dimension profiles and fractional Brownian motion. (with D.
Khoshnevisan). Math. Proc. Cambridge Philo.
Soc.
145 (2008), 205--213.
[18]. Local
times of multifractional Brownian sheets.
(with
M. Meerschaert
and D. Wu).
Bernoulli 14(3) (2008), 865--898.
[17]. Joint continuity of
the local times of fractional Brownian sheets. (with Antoine Ayache and
D. Wu). Ann.
Inst. H.
Poincare Probab. Statist. 44 (2008), 727--748.
[16].
Large deviations for local time fractional Brownian
motion and applications. (with
M. M. Meerschaert and E. Nane).
J. Math. Anal. Appl. 346 (2008), 432--445. [The original
publication is available at
www.elsevier.com/locate/jmaa]
[15]. Packing dimension of the
range of a Levy process. (with D. Khoshnevisan). Proc. Amer. Math. Soc. 136
(2008), 2597--2607.
[14]. Hausdorff dimension of the
contours of symmetric additive Levy
processes. (with D.
Khoshnevisan and N.-R.
Shieh). Probab. Th. Rel. Fields. 140 (2008), 169--193.
[The original publication is available at
www.springerlink.com.]
[13].
Sample path properties of bifractional Brownian motion.
(with
Ciprian A. Tudor).
Bernoulli 13 (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
[44]. The 6th International
Conference on Levy Processes and Applications. Dresden, Germany, July 26--30,
2010.
[43]. The 33rd Conference on Stochastic
Processes and Their Applications. Berlin, Germany, July 27--31, 2009.
[42]. International Conference
on Self-Similarity of Stochastic Processes and Its Applications. Angers, France,
July 20--24, 2009.
[41]. The Third International
Conference on Stochastic Analysis and Its Applications.
Beijing Instittute of Technology, Beijing, China, July 13--17, 2009.
[40]. IMS-China International
Conference on Statistics and Probability. Weihai, China, July 3--6, 2009.
[39]. The First IMS Asia Pacific Rim Meeting.
Seoul, Korea, June 28--July 1, 2009.
[38]. Spring School on
Random Differential Equations and Gaussian Fields. Chateau de Mons, France,
June 15--19, 2009.
[37]. The Second Midwest
Statistics Research Colloquium
University of Chicago, March 27--28, 2009.
[36]. The 15th
Workshop on Stochastic Geometry, Stereology and Image Analysis.
Heinrich-Fabri-Institute in Blaubeuren, Germany, March 22--27, 2009.
[35].
The Workshop on Infinitely Divisible Processes.
CIMAT, Guanajuato, Mexico, March 15--21, 2009.
[34].
The Workshop on Random Fields and Stochastic Geometry.
The Banff International Research Station for Mathematical
Innovation and Discovery (BIRS), Canada, February 22--27, 2009.
[33].
The Workshop on Models and Images of Random Media. Paris,
January 12--16 , 2009.
[32].
The First Joint AMS-SMS Meeting. Fudan University, Shanghai, China,
December 17--21, 2008.
[31]. The Seventh
Northeast Probability Seminar., Courant Institute of Mathematics at New York University,
November 20--21, 2008.
[30].
The AMS 2008 Fall Southeastern Sectional Meeting. University of Alabama in Huntsville,
October 24--26, 2008.
[29]. The Thirtieth Midwest Probability
Colloquium. Northwestern University, October 23--25, 2008.
[28].
Fractal Geometry and Stochastics, 4. Greifswald, Germany, September 8-12, 2008.
[27]. The CBMS Conference on Malliavin
Calculus and Its Applications. Kent State University, August 7--12, 2008.
[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.
[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.
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