Lihu XU
徐禮虎 Assistant Professor |

Academic Qualifications

- PhD in Mathematics, Imperial College London, UK (2007)
- Master in Mathematics, Peking University, Beijing (2004)
- Bachelor in Mathematics, Shandong University, Jinan (2001)

Working Experience

- 01/2014-present Assistant Professor, University of Macau, Macau.
- 09/2013-12/2013 Research Faculty, Boston College, Boston, US.
- 09/2011-09/2013 Lecturer (permanent position), Brunel University, London, UK.
- 10/2010-09/2011 Postdoc, TU Berlin, Berlin, Germany.
- 09/2010-10/2010 Academic Visitor, Hausdorff Center for Mathematics, Bonn, Germany.
- 10/2008-08/2010 Postdoc, EURANDOM, Eindhoven, the Netherlands.
- 09/2007-08/2008 Postdoc, Hausdorff Center for Mathematics, Bonn, Germany.

Teaching

Courses

- Introduction to Real Analysis and Hilbert Spaces (University of Macau)
- Topics in Probability Theory (University of Macau)
- Probability and Statistics (University of Macau)
- Probability Theory (University of Macau)
- Introduction to Stochastic Calculus (University of Macau)
- Mathematical Analysis (Brunel University London)
- Probability Theory (Brunel University London)
- Final year project: Quantile regression (Brunel University London)
- Introduction to stochastic partial differential equations (TU Berlin)

PhD students

- Ms. Fang XIE (2015--2018): L1 penalized methods in high-dimensional regressions and its theoretical properties
- Mr. Peng CHEN (2017--):
- Mr. Xing-Hu JING (2017--):
- Ms. Xin XU (2017--): Joint with Prof. Xuefeng WANG at SUSTech
- Mr. Jianya LU (2018--):

Master students

- Ms. Fang XIE (2013---2015): High dimensional lasso regressions
- Mr. Libang DENG (2013---2015): Asset pricing models and an SPDEs
- Mr. Zhilei FAN (2015---2017): False discovery rate and self-normalized Cramer type moderate deviations
- Ms. Qiuran YAO (2016---):
- Ms. Jinjin YU (2018--):
- Mr. Xiang LI (2018--):

Final year project students

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

Research

Research Interests

- Stochastic PDEs, Ergodic Theory, Levy Processes, Large (Moderate) Deviations, Limit Theorems, Theory on High Dimensional Statistics

Research Grants

**External Grants**

- Stochastic Gierer-Meinhardt and Schnakenberg models in biology, PI, FDCT/049/2014/A1, 20/01/2015-19/01/2017.
- Large and moderate deviations for empirical measure of stochastic partial differential equations, PI, FDCT/030/2016/A1, 01/09/2016-31/08/2019.
- Some optimization problems with model ambiguity and information incompleteness, PI, FDCT/025/2016/A1, 01/09/2016-31/08/2019.
- Ergodicity of Stochastic PDEs driven highly degenerate pure jump noises, PI, NSFC 11571390 (general project 国家自然科学基金面上项目), 01/01/2016-31/12/2019.
- Fluctuation of entropy production rate, PI, FDCT 038/2017/A1.

**Internal Grants**

- Large deviation of stochastic Gierer-Meinhardt and Schnakenberg models, PI, SRG2013-00064-FST, 01/01/2014-31/01/2015.
- Stochastic Gierer-Meinhardt and Schnakenberg models in biology, PI, MRG017/XLH/2015/FST, 01/08/2014-31/07/2015.
- Applications of the LASSO and the Squre-root LASSO methods to correlated big data, PI, MYRG2016-00025-FST, 01/04/2015-31/03/2018.
- 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.
- High dimensional probability approximations, PI, MYRG2018-00133-FST, 01/01/2019-31/12/2021.

Publications

Journal Papers Under Revision

- Ran Wang; Jie Xiong and
**Lihu Xu***: Large deviation principle of occupation measures for non-linear monotone SPDEs,**S***cience China Mathematics.*

Journal Papers

**Lihu Xu:**Approximation of stable law in Wasserstein-1 distance by Stein's method,*Annals of Applied Probability*(**),**https://www.imstat.org/journals-and-publications/annals-of-applied-probability/annals-of-applied-probability-future-papers/

This paper**‘***breaks new grounds on the Stein’s famous method and also opens up many new interesting research problems’*(from a 5 pages’ referee’s report)*.*- Xiao Fang; Qi-Man Shao and
**Lihu Xu*:**Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula,https://link.springer.com/article/10.1007%2Fs00440-018-0874-5*Probability Theory and Related Fields,* - Zhao Dong; Feng-Yu Wang and
**Lihu Xu***: Irreducibility and asymptotics of stochastic Burgers equation driven by alpha-stable processes,*Potential Analysis,* **Lihu Xu**: Singular integrals of stable subordinator,, Vol. 139, 115-118, 2018.*Statistics & Probability Letters*- Xiaobin Sun, Yimin Xiao,
**Lihu Xu***and Jianliang Zhai: Uniform dimension results for a family of Markov processes,, Vol. 24 4B, 3924-3951, 2018.*Bernoulli* - Ran Wang and
**Lihu Xu***: Asymptotics for stochastic reaction-diffusion equation driven by subordinate Brownian motions,, Vol. 128, 5, 1772-1796, 2018.*Stochastic Processes and Their Applications* - Fang Xie,
**Lihu Xu***and Youcai Yang: Lasso for sparse linear regression with exponentially β-mixing errors., 125 (2017), 64–70.*Statistics and Probability Letters* - 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. **Lihu Xu**, Wen Yue and Tusheng Zhang: Smooth densities of the laws of perturbed diffusion processes,*Statistics and Probability Letters**,*119 (2016), 55–62.- 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 Physics** - Xiao-Hong Chen, Qi-Man Shao, Wei Biao Wu and
**Lihu Xu**: Self-normalized Cramer Type Moderate Deviations under Dependence,, 44 (2016), no. 4, 1593–1617.*Annals of Statistics* - 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. - Zhao Dong, Symon Peszat and
**Lihu Xu***: On some smoothening effects of the transition semigroup of a Levy process,*Journal of Mathematical Analysis and Applications**,*434 (2016), no. 2, 1566–1580. - Matthias Winter,
**Lihu Xu***, Jianliang Zhai and Tusheng Zhang: The dynamics of the stochastic shadow Gierer-Meinhardt system,*Journal of Differential Equations* - Fang Li and
**Lihu Xu***: Finite time blowup of the stochastic shadow Gierer-Meinhardt System,, 20 (2015).*Electronic Communication on Probability* - Feng-Yu Wang,
**Lihu Xu**and Xicheng Zhang: Gradient estimates for SDEs driven by multiplicative Levy noise,, 269 (2015), 3195–3219.*Journal of Functional Analysis* - Ran Wang and
**Lihu Xu***: Asymptotics of the Entropy Production Rate for d-Dimensional Ornstein–Uhlenbeck Processes., 160 (2015), no. 5, 1336–1353.*Journal of Statistical Physics* - Feng-Yu Wang and
**Lihu Xu**: Log-Harnack inequality for Grushin type semigroup,, 30 (2014), no. 2, 405-418.*Revista Mathematica Iberoamericna* **Lihu Xu**: Exponential mixing for 2D SDEs forced by degenerate Levy noises,14 (2014), no. 2, 249-272.*Journal of Evolution Equations*- Zhao Dong,
**Lihu Xu***and Xicheng Zhang: Exponential ergodicity of stochastic Burgers equations forced by alpha-stable processes,, (2014), no. 4, 929-949.*Journal of Statistical Physics* **Lihu Xu**: Ergodicity of stochastic real Ginzburg-Landau equations forced by alpha-stable noises,, 123, no 10, (2013), 3710-3736.*Stochastic Processes and their Applications*- 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. - Sergio Albeverio, Arnaud Debussche and
**Lihu Xu***: Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises,**Applied Mathematics & Optimizations** - Enrico Priola, Armen Shirikyan,
**Lihu Xu***and Jerzy Zabczyk: Exponential ergodicity and regularity for equations with Levy noise,, 122, 1 (2012), 106-133.*Stochastic Processes and their Applications* - Zhao Dong,
**Lihu Xu**and Xicheng Zhang: Invariance measures of stochastic 2D Navier-Stokes equations driven by alpha-stable processes,, Vol. 16 (2011), 678-688.*Electronic Communication on Probability* **Lihu Xu**: A modified log-Harnack inequality and asymptotically strong Feller property,, 11 (2011), 925-942.*Journal of Evolution Equations*- 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. - Enrico Priola,
**Lihu Xu**and J. Zabczyk: Exponential mixing for SPDEs with Levy noises,, 11 (2011), 521-534.*Stochastic and Dynamics* - Marco Romito and
**Lihu Xu**: Ergodicity of 3D stochastic Navier-Stokes equations driven by mildly degenerate noises,, 121, (2011), no. 4, 673-700.*Stochastic Processes and their Applications* **Lihu Xu**and Boguslaw Zegarlinski: Existence and exponential mixing of the alpha-stable systems with unbounded interactions,, Vol. 15 (2010), 1994-2018.*Electronic Journal of Probability***Lihu Xu**and Boguslaw Zegarlinski: Ergodicity of finite and infinite dimensional alpha-stable systems,, 27 (2009), no. 4, 797--824.*Stochastic Analysis and its Applications*- Robert Olkiewicz,
**Lihu Xu**and Boguslaw Zegarlinski: Nonlinear problems in infinite interacting particle systems,*Infinite Dimensional Analysis Quantum Probability and Related Topics*

Mini-Courses:

- Approximation of stable law in Wasserstein-1 distance by Stein's method
**,**Warsaw, 07-08/06/2018.*Banach International Mathematical Research Center*, - Approximation of stable law in Wasserstein-1 distance by Stein's method
**,**Wuhan, 02-03/04/2018.*Wuhan University*,

Keynote Talks:

- Approximation of stable law by Stein’s method,

, Changchun, 09/2017.*2nd Sino-Russian probability and large sample conference* - Approximation of stable law,

, Chengdu, 10/2018.*11th Congress of Probability and Statistics in China*

Selected invited talks:

- Approximations of probability measures,

Kuala Lumpur, 2019.*World Congress in Statistics*, - Lindeberg’s method for stable central limit theorem,

, Beijing, 09/2018*New Trends in Stochastic Analysis Conference* - Talk 1: A Malliavin-Stein approach for multivariate approximations in Wasserstein distance,

Talk 2: Approximation of stable law in Wasserstein-1 distance by Stein's method,

, Taipei, 07/2018*The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications* - A Malliavin-Stein approach for multivariate approximations in Wasserstein distance,

, Gothenburg, 06/2018.*Conference of Stochastic Processes and Their Applications* - Approximation of stable law,

, Beijing, 2017.*International conference on probability theory and statistical physics* - Convergence rate of stable law,

, Crakow, 2017.*CNRS-IMPAN mathematics summer institute conference* - Irreducibility of stochastic Burgers equations,

, Wuhan, 2017.*International conference of Markov processes and their related fields* - The long time behaviour of stochastic system with singular coefficients,

, Shanghai, 2016.*10th ICSA international conference* - The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields,

, Hefei, 08/2016.*Workshop of Young Probabilists* - The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields,

, Shanghai, 07/2016.*Conference of Stochastic Dynamics and SPDEs* - Large deviation for monotone SPDEs,

, Hong Kong, 06/2016.*The 4th Institute of Mathematical Statistics Asia Pacific Rim Meeting* - Large deviation for monotone SPDEs,

Beijing, 06/2016.*8th International Conference on Stochastic Analysis and Applications,* - Asymptotics of the entropy production rate for d-dimensional Ornstein-Uhlenbeck processes,

Kunmin, 07/2015.*2015 IMS-China International Conference on Statistics and Probability,* - Asymptotics of the entropy production rate for $d$-dimensional Ornstein-Uhlenbeck processes,

Beijing, 07/2015.*Workshop of Young Probabilists at Peking University,* - Asymptotics of the entropy production rate for $d$-dimensional Ornstein-Uhlenbeck processes,

Wuhan, 05/2015.*Workshop of Young Probabilists,* - Exponential mixing for stochastic 3D Navier-Stokes equations driven by mildly degenerate noises,

NUS, Singapore, 12/2014.*IMS Probability Day,* - Exponential mixing for stochastic 2d SDEs driven by degenerate noises,

, Xuzhou, 12/2014.*International Conference on SPDEs* - Stochastic shadow Gierer-Meinhardt system,

Hefei, 09/2014.*International Conference on SPDEs,*

Services

Professional Services

- External referees:
- Grant applications from EPSRC of UK, 2018
- Grant applications from NSF of China, 2016-now
- Grant applications from TianYuan Foundation of Mathematics, 2015

- Referees for >30 papers in >15 journals: Journal of American Mathematical Society, Journal of Illinois Mathematics, Stochastic Processes and Their Applications, Applied Mathematics & Optimization, Statistics & Probability Letters, Sciences in China-Mathematics, Communications in Pure and Applied Analysis, Mathematische Nachrichten, Journal of Computational and Applied Mathematics, Journal of Applied Probability, Journal of Theoretical Probability, Electronic Communications in Probability, Journal of Mathematical Analysis and its Applications, East Asian Journal on Applied Mathematics, Econometrics Review.
- Organizers
- The session ’Recent Advances in Stochastic Processes and its Applications’, World Congress of Statistics, 2013
- The workshop ’Probability Theory and its Applications’, University of Macau, 2015
- The session ’Statistical Physics’ at ’Joint Annual Conference of Physics Societies in Greater Bay Area’, 2018
- The workshop ’Stein’s method and its related topics’, University of Macau, 2018

- Reviewer of American Mathematical Society, 2011-now
- Member of Macau Bioinformatics Association Committee, 2018-now
- Junior Scientific Leader of Banach International Mathematical Center, 2018
- Junior Member of Financial Mathematics Committee of SIAM China, 2017-now

University Services

- Fellow of Chao Kuang Piu College (2015-).
- Member of new academic staff club (2014).
- Member of final year project oral examination committee, (2015-).
- Member of principal recommendation students admission committee, (2015-).
- Leader of minor program of mathematics, (2015-).
- Member of master student recruitment committee, (2015-).
- Member of 12 PhD advisory committees
- Assessment Panel of 13 PhD qualify examinations
- Working secretary of 3 PhD oral defenses
- 'Tea with professors' activity (2014, 2017)
- Leader of UM undergraduates’ academic visit to Sun Yat-Sen University
- Supervision of 2 summer research of undergraduates
- Supervision of 2 honor final year projects
- Supervision of 4 final year projects

Honors

- Junior Scientific Leader, Banach International Mathematical Center, 2018
- Research Excellence Award of FST, UM, Macau, 2016-2017.
- DAAD Research Fellowship, Germany, 2006.
- International Student Scholarship, Imperial College, UK, 2004-2007
- 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