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Stein’s Method for Asymmetric α -stable Distributions, with Application to the Stable CLT Journal article
Journal of Theoretical Probability, 2020
Authors:  Chen,Peng;  Nourdin,Ivan;  Xu,Lihu
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Asymmetric α-stable distribution  Fractional Laplacian  Leave-one-out approach  Normal attraction  Stable central limit theorem  Stein’s method  
Large deviation for two-time-scale stochastic burgers equation Journal article
Stochastics and Dynamics, 2020
Authors:  Sun,Xiaobin;  Wang,Ran;  Xu,Lihu;  Yang,Xue
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large deviation  slow-fast  Stochastic Burgers equation  weak convergence  
Approximation to stable law by the Lindeberg principle Journal article
Journal of Mathematical Analysis and Applications, 2019,Volume: 480,Issue: 2
Authors:  Chen,Peng;  Xu,Lihu
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A Kolmogorov forward equation  Asymmetric α-stable distribution  Stable central limit theorem  The Lindeberg principle  
Multivariate approximations in Wasserstein distance by Stein’s method and Bismut’s formula Journal article
Probability Theory and Related Fields, 2019,Volume: 174,Issue: 3-4,Page: 945–979
Authors:  Xiao Fang;  Qi-Man Shao;  Lihu Xu
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Bismut's Formula  Multivariate Approximation  Rate Of Convergence  Stein’s Method  Wasserstein Distance  Langevin Algorithm  Malliavin Calculus  
Exponential mixing for SPDEs driven by highly degenerate lévy noises Journal article
Illinois Journal of Mathematics, 2019,Volume: 63,Issue: 1,Page: 75-102
Authors:  Sun,Xiaobin;  Xie,Yingchao;  Xu,Lihu
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Approximation of stable law in Wasserstein-1 distance by Stein’s method1 Journal article
Annals of Applied Probability, 2019,Volume: 29,Issue: 1,Page: 458-504
Authors:  Xu,Lihu
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L1 discrepancy  Normal domain of attraction of stable law  Stable approximation  Stein’s method  Wasserstein-1 distance (W1 distance)  α-stable processes  
Approximation of stable law in Wasserstein-1 distance by Stein’s method Journal article
ANNALS OF APPLIED PROBABILITY, 2019,Volume: 29,Issue: 1,Page: 458-504
Authors:  Xu, Lihu
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Stable Approximation  Wasserstein-1 Distance (W-1 Distance)  Stein's Method  L-1 Discrepancy  Normal Domain Of Attraction Of Stable Law  Alpha-stable Processes  
Sparse poisson regression with penalized weighted score function Journal article
Electronic Journal of Statistics, 2019,Volume: 13,Issue: 2,Page: 2898-2920
Authors:  Jia,Jinzhu;  Xie,Fang;  Xu,Lihu
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Image reconstruction  Moderate deviation  Poisson regression  Tuning-free  ℓ1 consistency  ℓ1 penalization  
Uniform dimension results for a family of Markov processes Journal article
BERNOULLI, 2018,Volume: 24,Issue: 4B,Page: 3924-3951
Authors:  Sun, Xiaobin;  Xiao, Yimin;  Xu, Lihu;  Zhai, Jianliang
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Cover Principles  Markov Processes  Uniform Hausdorff Dimension  
Uniform dimension results for a family of markov processes Journal article
Bernoulli, 2018,Volume: 24,Issue: 4B,Page: 3924-3951
Authors:  Sun,Xiaobin;  Xiao,Yimin;  Xu,Lihu;  Zhai,Jianliang
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Cover principles  Markov processes  Uniform Hausdorff dimension