Lihu XU  徐禮虎
Assistant Professor

Academic Qualifications | Working Experience | Teaching | Research | Publications | 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 student

  1. Ms. Fang XIE (2015--): Ms. XIE is now working under my supervision on the applications of probability methods (e.g. Concentration inequalities, Cramer type moderate deviation, high dimensional Stein’s method) to high dimension Statistics problems (e.g. lasso, square-root lasso, sparse regressions of generalized linear models, dictionary learning).

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


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. 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.
  5. Large and moderate deviations for empirical measure of stochastic partial differential equations, PI, FDCT/030/2016/A1, 01/09/2016-31/08/2019.
  6. 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.

  1. (With F. Xie and Y. Yang) Lasso for sparse linear regression with exponentially β-mixing errors. Statistics and Probability Letters, 125 (2017), 64–70.
  2. (With R. Wang and J. Xiong)  Irreducibility of stochastic real Ginzburg-Landau equation driven by alpha-stable noises and applications, Bernoulli, 23 (2017), no. 2, 1179–1201.
  3. (With W. Yue and T. Zhang) Smooth densities of the laws of perturbed diffusion processes, Statistics and Probability Letters, 119 (2016), 55–62.
  4. (With Y. Chen, H. Ge and J. Xiong) The large deviation principle and steady-state fluctuation theorem for the entropy production rate of a stochastic process in magnetic fields, Journal of Mathematical Physics, 57 (2016), no. 7, 073302, 16 pp.
  5. (With X. Chen, Q.M. Shao and W.B. Wu) Self-normalized Cramer Type Moderate Deviations under Dependence, Annals of Statistics, 44 (2016), no. 4, 1593–1617.
  6. (With F. Wang and J. Xiong) Asymptotics of sample entropy production rate for stochastic differential equations, Journal of Statistical Physics, 163 (2016), no. 5, 1211–1234.
  7. (With Z. Dong and S. Peszat) On some  smoothening effects of the transition semigroup  of  a  Levy process, Journal of Mathematical Analysis and Applications, 434 (2016), no. 2, 1566–1580.
  8. (with M. Winter, J. Zhai and T. Zhang) The dynamics of the stochastic shadow Gierer-Meinhardt system, Journal of Differential Equations 260 (2016), no. 1, 84–114.
  9. (with F. Li) Finite time blowup of the stochastic shadow Gierer-Meinhardt System, Electronic Communication on Probability, 20 (2015).
  10. (With F. Wang and X. Zhang) Gradient estimates for SDEs driven by multiplicative Levy noise, Journal of Functional Analysis, 269 (2015), 3195–3219.
  11. (with R.Wang) Asymptotics of the Entropy Production Rate for d-Dimensional Ornstein–Uhlenbeck Processes. Journal of Statistical Physics, 160 (2015), no. 5, 1336–1353.
  12. (with F. Wang) Log-Harnack inequality for Grushin type semigroup, Revista Mathematica Iberoamericna, 30 (2014), no. 2, 405-418.
  13. Exponential mixing for 2D SDEs forced by degenerate Levy noises, Journal of Evolution Equations 14 (2014), no. 2, 249-272.
  14. (with Z. Dong and X. Zhang) Exponential ergodicity of stochastic Burgers equations forced by alpha-stable processes, Journal of Statistical Physics, (2014), no. 4, 929-949.
  15. Ergodicity of stochastic real Ginzburg-Landau equations forced by alpha-stable noises, Stochastic Processes and their Applications, 123, no 10, (2013), 3710-3736.
  16. (with F. Wang) 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.
  17. (with S. Albeverio and A. Debussche) Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises, Applied Mathematics & Optimizations, 66, 2 (2012), 273-308.
  18. (with E.Priola, A.Shirikyan and J.Zabczyk), Exponential ergodicity and regularity for equations with Levy noise, Stochastic Processes and their Applications, 122, 1 (2012), 106-133.
  19. (with Z. Dong and X. Zhang) Invariance measures of stochastic 2D Navier-Stokes equations driven by alpha-stable processes, Electronic Communication on Probability, Vol. 16 (2011), 678-688.
  20. A modified log-Harnack inequality and asymptotically strong Feller property, Journal of Evolution Equations, 11 (2011), 925-942.
  21. (with F. Wang and J. Wu) Log-Harnack inequality of stochastic Burgers equations, Journal of Mathematical Analysis and Applications, 384 (2011), 151--159.
  22. (with E. Priola and J. Zabczyk) Exponential mixing for SPDEs with Levy noises, Stochastic and Dynamics, 11 (2011), 521-534.
  23. (with M. Romito) Ergodicity of 3D stochastic Navier-Stokes equations driven by mildly degenerate noises, Stochastic Processes and their Applications, 121, (2011), no. 4, 673-700.
  24. (with B. Zegarlinski) Existence and exponential mixing of the alpha-stable systems with unbounded interactions, Electronic Journal of Probability, Vol. 15 (2010), 1994-2018.
  25. (with B. Zegarlinski) Ergodicity of finite and infinite dimensional alpha-stable systems, Stochastic Analysis and its Applications, 27 (2009), no. 4, 797--824.
  26. (with R. Olkiewicz and B. Zegarlinski) Nonlinear problems in infinite interacting particle systems, Infinite Dimensional Analysis Quantum Probability and Related Topics, 11 (2008), no. 2, 179--211.

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