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Research Interests

Stochastic processes and random fields: Gaussian and stable random fields,  fractional Lévy fields, self-similar processes, Lévy processes, additive Lévy processes.

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

Extreme value theory: Gaussian and related random fields.

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

Seminars

Colloquiua of Department of Statistics and Probability. Tuesday, 10:20--11:10AM

Probability at Michigan State. Thursday, 3:00--3:50PM

Editorial Service

Co-Editor in Chief, Statistics & Probability Letters, July, 2011 -- present.

Managing Editor, Journal of Fractal Geometry, July, 2013 -- present.

Associate Editor, Science China: Mathematics, January, 2015 -- present.

Survey Articles

[4]. Recent developments on fractal properties of Gaussian random fields.  In: Further Developments in Fractals and Related Fields. (Julien Barral and Stephane Seuret, editors) pp. 255--288, Springer, New York, 2013.

[3]. Properties of local nondeterminism of Gaussian and stable random fields and their applications.  Ann. Fac. Sci. Toulouse Math. XV (2006), 157--193.

[2]. Additive Levy 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 Recent Publications

[60]. Polarity of points for Gaussian random fields. (with R. Dalang and C. Mueller), Submitted, 2015.

[59]. Tail asymptotics of extremes for bivariate Gaussian random fields. (with Y. Zhou), Submitted, 2015.

[58]. Intermittency and multifractality: A case study via parabolic stochastic PDEs. (with D. Khoshnevisan and K. Kim), Submitted, 2015.

[57]. Sample paths of the solution to the fractional-colored stochastic heat equation. (with C. Tudor), Submitted, 2015.

[56]. On the double points of operator stable Lévy processes. (with T. Luks), J. Theoret. Probab., to appear.

[55]. Weak existence of a solution to a differential equation driven by a very rough fBm. (with D. Khoshnevisan, J. Swanson and L. Zhang), Submitted. 2014.

[54]. Harmonizable fractional stable fields: local nondeterminism and joint continuity of the local times. (with A. Ayache), Stoch. Process. Appl., to appear.

[53]. The mean Euler characteristic and excursion probability of Gaussian random fields. (with D. Cheng), Ann. Appl. Probab., to appear.

[52]. Excursion probability of Gaussian random fields on sphere. (with D. Cheng), Bernoulli, to appear.

[51].Smoothness of local times and self-intersection local times of Gaussian random fields. (with Z. Chen and D. Wu), Frontiers Math. China 10 (2015), 777--805.

[50]. Exact moduli of continuity for operator scaling Gaussian random fields. (with Yuqiang Li and Wensheng Wang), Bernoulli 21 (2015), 930--956.

[49]. Brownian motion and thermal capacity. (with D. Khoshnevisan), Ann. Probab. 45 (2015), 405--434.

[48]. Generalized dimensions of images of measures under Gaussian processes. (with K.J. Falconer), Adv. Math. 252 (2014), 492--517.

[47]. Discrete fractal dimensions of the ranges of random walks in $\Z^d$ associate with random conductances. (with Xinghua Zheng), Probab. Th. Rel. Fields 156 (2013), 1--26.

[46]. A class of fractional Brownian fields from branching systems and their regularity properties. (with Yuqiang Li), Infi. Dim. Anal. Quan. Probab. Rel. Topics 16, (2013).

[45]. Tail estimation of the spectral density under fixed-domain asymptotics. (with Chae-Young Lim and Wei-Ying Wu), J. Multivar. Anal. 116 (2013), 74--91.

[44]. Fractal dimension for continuous time random walk limits.  (with M. M. Meerschaert and E. Nane), Statist. Probab. Letters 83 (2013), 1083--1093.

[43]. Hitting probability and packing dimensions of the random covering sets. (with Bing Li and Narn-Rueih Shieh). In: Applications of Fractals and Dynamical Systems in Science and Economics, (David Carfi, Michel L. Lapidus, Erin P. J. Pearse, and Machiel van Frankenhuijsen, editors), American Mathematical Society, 2013.

[42]. Fernique-type inequalities and moduli of continuity of anisotropic Gaussian random fields. (with M.M. Meerschaert and Wensheng Wang), Trans. Amer. Math. Soc. 365 (2013), 1081--1107.

[41]. On intersections of independent anisotropic Gaussian random fields. (with Zhenlong Chen), Sci. China Math. 55 (2012), 2217--2232.

[40]. Packing dimension profiles and Levy processes. (with D. Khoshnevisan and R. Schiling), Bull. London Math. Soc. 44 (2012), 931--943.

[39]. Occupation time fluctuations of weakly degenerated branching systems.  (with Yuqiang Li), J. Theoret. Probab, 25 (2012), 1119--1152.

[38]. $\alpha$-time fractional Brownian motion: PDE connections and local times. (with E. Nane and D. Wu), Esaim: Probab.& Stat. 16 (2012), 1--24.

[37]. Critical Brownian sheet does not have double points. (with R. C. Dalang, D. Khoshnevisan, E. Nualart and D. Wu), Ann. Probab. 40 (2012), 1829--1859

[36]. Spectral conditions for strong local nondeterminism and exact Hausdorff measure of ranges of Gaussian random fields. (with N. Luan), J. Fourier Anal. Appl. 18 (2012), 118--145.

[35].  Multiparameter multifractional Brownian motion: local nondeterminism and joint continuity of the local times. (with A. Ayache and N.-R. Shieh), Ann. Inst. H. Poincare Probab. Statist. 47 (2011), 1029--1054.

[34]. Multivariate operator-self-similar random fields. (with Yuqiang Li), Stoch. Process. Appl. 121 (2011), 1178--1200.

[33]. Fractal and smoothness properties of anisotropic Gaussian models. (with Yun Xue), Frontiers Math. 6 (2011), 1217--1246.

[32]. Packing dimension results for anisotropic Gaussian random fields. (with A. Estrade and D. Wu), Comm. Stoch. Anal.  5 (2011), 41--64.

[31]. On local times of anisotropic Gaussian random fields. (with D. Wu), Comm. Stoch. Anal. 5 (2011), 15--39.

[30]. Properties of strong local nondeterminism and local times of stable random fields. Seminar on Stochastic Analysis, Random Fields and Applications VI.  pp. 279--310. Progr. Probab., 63, Birkh\"auser, Basel , 2011.

[29]. Hausdorff and packing dimensions of the images of random fields. (with N.-R. Shieh), Bernoulli 16 (2010), 926--952.

[28]. Regularity of intersection local times of fractional Brownian motions. (with D. Wu). J. Theoret. Probab. 23 (2010), 972--1001.

[27]. On uniform modulus of continuity of random fields. Monatsh. Math. 159 (2010), 163--184.

[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, 145 (2009), 459--515. [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]. Levy 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 Levy 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.

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