Lihu XU  徐禮虎
Assistant Professor

Academic Qualifications | Working Experience | Teaching | Research | Publications | Services | Honors | Contact Details

Academic Qualifications
Working Experience


  1. Introduction to Real Analysis and Hilbert Spaces (University of Macau)
  2. Topics in Probability Theory (University of Macau)
  3. Probability and Statistics (University of Macau)
  4. Probability Theory (University of Macau)
  5. Introduction to Stochastic Calculus (University of Macau)
  6. Mathematical Analysis (Brunel University London)
  7. Probability Theory (Brunel University London)
  8. Final year project: Quantile regression (Brunel University London)
  9. Introduction to stochastic partial differential equations (TU Berlin)

PhD students

  1. Ms. Fang XIE (2015--2018): Visiting assistant professor at Wuhan University
    Thesis: .
  2. Peng CHEN (2017--):
  3. Xing-Hu JING (2017--):
  4. Xin XU (2017--): Joint with Prof. Xuefeng WANG at SUSTech

Master students

  1. Ms. Fang XIE (2013---2015): High dimensional lasso regressions
  2. Mr. Libang DENG (2013---2015): Asset pricing models and an SPDEs
  3. Mr. Zhilei FAN (2015---2017): False discovery rate and self-normalized Cramer type moderate deviations
  4. Ms. Qiuran YAO (2016---):

Final year project students

  1. Mr. Yong MA (2015): Least angle regression and square-root lasso
  2. Mr. Yiyuan YU (2016): False discovery rate in Statistics
  3. Mr. Mu LI (2017): Fused Kolmogorov filter: a nonparametric model-free screening method (honor project)
  4. Mr. Jingxiu WANG (2017): Dictionary identification-sparse matrix-factorization via l_1 minimization
  5. Mr. Bo WU (2018): High dimensional negative binomial regression (honor project)


Research Interests

Research Grants

  1. Large deviation of stochastic Gierer-Meinhardt and Schnakenberg models, PI, SRG2013-00064-FST, 01/01/2014-31/01/2015.
  2. Stochastic Gierer-Meinhardt and Schnakenberg models in biology, PI, FDCT/049/2014/A1, 20/01/2015-19/01/2017.
  3. Applications of the LASSO and the Squre-root LASSO methods to correlated big data, PI, MYRG2016-00025-FST, 01/04/2015-31/03/2018.
  4. Large and moderate deviations for empirical measure of stochastic partial differential equations, PI, FDCT/030/2016/A1, 01/09/2016-31/08/2019.
  5. Ergodicity of Stochastic PDEs driven highly degenerate pure jump noises, PI, NSFC 11571390 (general program 国家自然科学基金面上项目), 01/01/2016-31/12/2019.
  6. Applications of coupling method to studying the ergodicity of stochastic PDEs driven by degenerated pure jump Levy processes, PI, MYRG2016-00025-FST, 01/01/2017-31/12/2019.
  7. Fluctuation of entropy production rate, PI, FDCT 038/2017/A1, 01/09/2017-31/09/2020.


Journal Papers Under Revision

  1. Ran Wang; Jie Xiong and Lihu Xu*: Large deviation principle of occupation measures for non-linear monotone SPDEs, Science China Mathematics.
  2. Zhao Dong; Feng-Yu Wang and Lihu Xu*: Irreducibility and asymptotics of stochastic Burgers equation driven by alpha-stable processes,  Potential Analysis.

Journal Papers

  1. Lihu Xu: Approximation of stable law in Wasserstein-1 distance by Stein's method, Annals of Applied Probability (accepted). arXiv:1709.00805v3

    This paper breaks new grounds in the Stein’s famous method and opens up many new interesting research problems’ (from a 5 pages’ referee’s report).
  2. Xiao Fang; Qi-Man Shao and Lihu Xu*: Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula, Probability Theory and Related Fields (accepted). arXiv:1801.07815v2
  3. Lihu Xu: Singular integrals of stable subordinator, Statistics & Probability Letters, Vol. 139, 115-118, 2018.
  4. Xiaobin Sun, Yimin Xiao, Lihu Xu* and Jianliang Zhai: Uniform dimension results for a family of Markov processes, Bernoulli, Vol. 24 4B, 3924-3951, 2018.
  5. Ran Wang and Lihu Xu*: Asymptotics for stochastic reaction-diffusion equation driven by subordinate Brownian motions, Stochastic Processes and Their Applications, Vol. 128, 5, 1772-1796, 2018.
  6. Fang Xie, Lihu Xu* and Youcai Yang: Lasso for sparse linear regression with exponentially β-mixing errors. Statistics and Probability Letters125 (2017), 64–70.
  7. Ran Wang, Jie Xiong and Lihu Xu*: Irreducibility of stochastic real Ginzburg-Landau equation driven by alpha-stable noises and applications, Bernoulli, 23 (2017), no. 2, 1179–1201.
  8. Lihu Xu, Wen Yue and Tusheng Zhang: Smooth densities of the laws of perturbed diffusion processes, Statistics and Probability Letters, 119 (2016), 55–62. 
  9. Yong Chen, Hao Ge, Jie Xiong and Lihu Xu*: The large deviation principle and steady-state fluctuation theorem for the entropy production rate of a stochastic process in magnetic fields, Journal of Mathematical Physics57 (2016), no. 7, 073302, 16 pp.
  10. Xiao-Hong Chen, Qi-Man Shao, Wei Biao Wu and Lihu Xu: Self-normalized Cramer Type Moderate Deviations under Dependence, Annals of Statistics, 44 (2016), no. 4, 1593–1617. 
  11. Feng-Yu Wang, Jie Xiong and Lihu Xu*: Asymptotics of sample entropy production rate for stochastic differential equations, Journal of Statistical Physics, 163 (2016), no. 5, 1211–1234.
  12. Zhao Dong, Symon Peszat and Lihu Xu*: On some  smoothening effects of the transition semigroup  of  a  Levy process, Journal of Mathematical Analysis and Applications434 (2016), no. 2, 1566–1580.
  13. Matthias Winter, Lihu Xu*, Jianliang Zhai and Tusheng Zhang: The dynamics of the stochastic shadow Gierer-Meinhardt system, Journal of Differential Equations 260 (2016), no. 1, 84–114.
  14. Fang Li and Lihu Xu*: Finite time blowup of the stochastic shadow Gierer-Meinhardt System, Electronic Communication on Probability, 20 (2015).
  15. Feng-Yu Wang, Lihu Xu and Xicheng Zhang: Gradient estimates for SDEs driven by multiplicative Levy noise, Journal of Functional Analysis, 269 (2015), 3195–3219.
  16. Ran Wang and Lihu Xu*: Asymptotics of the Entropy Production Rate for d-Dimensional Ornstein–Uhlenbeck Processes. Journal of Statistical Physics, 160 (2015), no. 5, 1336–1353.
  17. Feng-Yu Wang and Lihu Xu: Log-Harnack inequality for Grushin type semigroup, Revista Mathematica Iberoamericna, 30 (2014), no. 2, 405-418.
  18. Lihu Xu: Exponential mixing for 2D SDEs forced by degenerate Levy noises, Journal of Evolution Equations14 (2014), no. 2, 249-272.
  19. Zhao Dong, Lihu Xu* and Xicheng Zhang: Exponential ergodicity of stochastic Burgers equations forced by alpha-stable processes, Journal of Statistical Physics, (2014), no. 4, 929-949.
  20. Lihu Xu: Ergodicity of stochastic real Ginzburg-Landau equations forced by alpha-stable noises, Stochastic Processes and their Applications, 123, no 10, (2013), 3710-3736.
  21. Feng-Yu Wang and Lihu Xu: Derivative Formula and Applications for Hyperdissipative Stochastic Navier-Stokes/Burgers Equations, Infinite Dimensional Analysis Quantum Probability and Related Topics, Vol. 15, No. 3 (2012), pp 19.
  22. Sergio Albeverio, Arnaud Debussche and Lihu Xu*: Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises, Applied Mathematics & Optimizations, 66, 2 (2012), 273-308.
  23. Enrico Priola, Armen Shirikyan, Lihu Xu* and Jerzy Zabczyk: Exponential ergodicity and regularity for equations with Levy noise, Stochastic Processes and their Applications, 122, 1 (2012), 106-133.
  24. Zhao Dong, Lihu Xu and Xicheng Zhang: Invariance measures of stochastic 2D Navier-Stokes equations driven by alpha-stable processes, Electronic Communication on Probability, Vol. 16 (2011), 678-688.
  25. Lihu Xu: A modified log-Harnack inequality and asymptotically strong Feller property, Journal of Evolution Equations, 11 (2011), 925-942.
  26. Feng-Yu Wang, Jiang-Lun Wu and Lihu Xu*: Log-Harnack inequality of stochastic Burgers equations, Journal of Mathematical Analysis and Applications, 384 (2011), 151--159.
  27. Enrico Priola, Lihu Xu and J. Zabczyk: Exponential mixing for SPDEs with Levy noises, Stochastic and Dynamics, 11 (2011), 521-534.
  28. Marco Romito and Lihu Xu: Ergodicity of 3D stochastic Navier-Stokes equations driven by mildly degenerate noises, Stochastic Processes and their Applications, 121, (2011), no. 4, 673-700.
  29. Lihu Xu and Boguslaw Zegarlinski: Existence and exponential mixing of the alpha-stable systems with unbounded interactions, Electronic Journal of Probability, Vol. 15 (2010), 1994-2018.
  30. Lihu Xu and Boguslaw Zegarlinski: Ergodicity of finite and infinite dimensional alpha-stable systems, Stochastic Analysis and its Applications, 27 (2009), no. 4, 797--824.
  31. Robert Olkiewicz, Lihu Xu and Boguslaw Zegarlinski: Nonlinear problems in infinite interacting particle systems, Infinite Dimensional Analysis Quantum Probability and Related Topics, 11 (2008), no. 2, 179--211.

Selected invited talks:

  1. Approximation of stable law (special invited speaker), 2nd Sino-Russian probability and large sample conference, Changchun, 2017.
  2. Approximation of stable law, International conference on probability theory and statistical physics, Beijing, 2017.
  3. Convergence rate of stable law, CNRS-IMPAN mathematics summer institute conference, Crakow, 2017. 
  4. Irreducibility of stochastic Burgers equations, International conference of Markov processes and their related fields, Wuhan, 2017.
  5. The long time behaviour of stochastic system with singular coefficients,  10th ICSA international conference, Shanghai, 2016.
  6. The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields, Workshop of Young Probabilists, Hefei, 08/2016.
  7. The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields, Conference of Stochastic Dynamics and SPDEs, Shanghai, 07/2016.
  8. Large deviation for monotone SPDEs, The 4th Institute of Mathematical Statistics Asia Pacific Rim Meeting, Hong Kong, 06/2016.
  9. Large deviation for monotone SPDEs, 8th International Conference on Stochastic Analysis and Applications, Beijing, 06/2016.
  10.  Asymptotics of the entropy production rate for d-dimensional Ornstein-Uhlenbeck processes, 2015 IMS-China International Conference on Statistics and Probability, Kunmin, 07/2015.
  11.  Asymptotics of the entropy production rate for $d$-dimensional Ornstein-Uhlenbeck processes, Workshop of Young Probabilists at Peking University, Beijing, 07/2015.
  12.  Asymptotics of the entropy production rate for $d$-dimensional Ornstein-Uhlenbeck processes, Workshop of Young Probabilists, Wuhan, 05/2015.
  13.  Exponential mixing for stochastic 2d SDEs driven by degenerate noises,  CAS, Beijing, 12/2014.
  14.  Exponential mixing for stochastic 3D Navier-Stokes equations driven by mildly degenerate noises, IMS Probability Day, NUS, Singapore, 12/2014.
  15.  Exponential mixing for stochastic 2d SDEs driven by degenerate noises,  International Conference on SPDEs, Xuzhou, 12/2014.
  16.  Stochastic shadow Gierer-Meinhardt system, International Conference on SPDEs, Hefei, 09/2014.
  17.  Exponential mixing for stochastic 3D Navier-Stokes equations driven by mildly degenerate noises, CAS, Beijing, 07/2014.
  18. Smoothness of the densities of degenerate SDEs driven by stable like noises, Workshop 'Stochastic Processes and Differential Equations in Infinite Dimensional Spaces', London, UK, 04/2014.

  1. Fellow of Chao Kuang Piu College (2015-).
  2. Member of new academic staff club (2014).
  3. Member of final year project oral examination committee, (2015-).
  4. Member of president recommendation students admission committee, (2015-).
  5. Leader of minor program of mathematics, (2015-).
  6. Member of master student recruitment committee, (2015-).
  7. Member of Ph.D. advisory committees: Mr. Wenfei WANG, Mr. Yiqi LIU, Ms. Jiayu ZHENG, Mr. Yashan ZHANG, Mr. Jianyu OU, Mr. Xucheng Meng, Mr. Xiaofei LI, Ms. Fang XIE, Ms. Qizhu LIANG, Ms. Hancheng GUO.
  8. Working secretary of PhD oral defenses: Dr. Weixiong MAI, Dr. Wenfei WANG.
  9. 'Tea with professors' activity (2014, 2017).
  10. Supervision of summer research of undergraduates: Mr. Jingxiu WANG (2016), Mr. Bo WU (2017).
  11. Supervision of honor final year projects: Mr. Mu LI (2016-2017), Mr. Bo WU (2017-2018).
  12. Supervision of final year projects: Mr. Yong MA (2015), Mr. Zhiyuan YU (2016), Mr. Jingxiu WANG (2017), Mr. Mu LI (2017), Bo WU (2018).
  13. Organizer of the workshop 'Probability and Statistics with Applications' (2015).

  1. Research Excellence Award of FST, UM, Macau, 2016-2017.
  2. Research Fellowship from Hausdorff Research Institute, Germany, 2007-2008.
  3. DAAD Research Fellowship, Germany, 2006.
  4. Overseas Research Students Awards, UK, 2004-2007.

Contact Details

Faculty of Science and Technology
University of Macau, E11
Avenida da Universidade, Taipa,
Macau, China

Room: E11-3075
Telephone: (853) 8822-4429
Fax: (853) 8822-2426
Email: lihuxu