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Professor Xuerong Mao

Mathematics and Statistics

Personal statement

He is an FRSE (Fellow of Royal Society of Edinburgh) and 1969 Chair of Statistics. He is also the Royal Society Wolfson Research Merit Award Holder.

He is a very active and extremely highly cited stochastic analyst (e.g. 18853 citations, h-index 66, i10-index 182 in Google Scholar on 19/12/2017).  He has made many influential contributions to the study of existence and long-term behaviour of solutions to nonlinear stochastic differential equations (SDEs). His seminal discoveries and new research directions include:

(1) Mao initiated a new research direction in the study of SDEs and Markov processes, developed a new set of analytical tools and established some fundamental results. His work is now the default reference in the area. Currently he is investigating the stability of highly nonlinear hybrid SDEs and stabilisation by feedback controls based on discrete-time observations.

(2) Mao and his coauthors were the first to study the strong convergence of numerical solutions of SDEs under a local Lipschitz condition. Their theory has formed the foundation for several recent very popular methods, including tamed Euler-Maruyama method and truncated Euler-Maruyama. Currently Mao is investigating the numerical stability of nonlinear SDEs under a local Lipschitz condition. This is a very hard and important problem.

(3) Mao discovered a surprising and far-reaching result: environmental Brownian noise can suppress explosions in population systems. This discovery has inspired many researchers to use SDEs as models of ecological and biological systems. His current research in this direction is concerned with linking experimental and theoretical analysis of biochemical systems subject to external noise. 

Publications

The truncated Milstein method for stochastic differential equations with commutative noise
Guo Qian, Liu Wei, Mao Xuerong, Yue Rong-xian
Journal of Computational and Applied Mathematics Vol 338, pp. 298-310, (2018)
http://dx.doi.org/10.1016/j.cam.2018.01.014
Convergence rate and stability of the truncated Euler-Maruyama method for stochastic differential equations
Hu Liangjian, Li Xiaoyue , Mao Xuerong
Journal of Computational and Applied Mathematics Vol 337, pp. 274-289, (2018)
http://dx.doi.org/10.1016/j.cam.2018.01.017
Explicit numerical approximations for stochastic differential equations in finite and infinite horizons : truncation methods, convergence in pth moment, and stability
Li Xiaoyue , Mao Xuerong, Yin George
IMA Journal of Numerical Analysis, (2018)
http://dx.doi.org/10.1093/imanum/dry015
Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique
Li Yuyuan, Lu Jianqiu, Kou Chunhai, Mao Xuerong, Pan Jiafeng
Statistics and Probability Letters, (2018)
http://dx.doi.org/10.1016/j.spl.2018.02.058
Stability of highly nonlinear neutral stochastic differential delay equations
Shen Mingxuan, Fei Weiyin, Mao Xuerong, Liang Yong
Systems and Control Letters, pp. 1-7, (2018)
Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation
Mao Wei, Hu Liangjian, Mao Xuerong
Discrete and Continuous Dynamical Systems - Series B, pp. 1-33, (2018)

more publications

Research interests

My research interests are mainly in the areas of stochastic differential equations and their applications. The reseach topics include the existence-and-uniqueness theory of the solutions to SDEs, stochastic stability, stochastic stabilisation by feedback controls, stationary distributions, asymptotic estimations, finite-time convergences of numerical solutions, asymptotic analysis of numerical solutions as well as stochastic modelling in finance, engineering, population systems, ecology etc.

Professional activities

Shanghai Normal University, China
Visiting lecturer
4/12/2015
International Workshop on Stochastic Differential Equations and Numerical Methods
Keynote/plenary speaker
13/11/2015
International Workshop on Stochastic Differential Equations and Numerical Methods
Organiser
13/11/2015
Stochastic Modelling in Housing Prices
Advisor
1/10/2015
SDE models in chemical systems
Advisor
1/10/2015
PhD External Examiner at Heriot-Watt University
External Examiner
28/9/2015

more professional activities

Projects

Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)
Mao, Xuerong (Principal Investigator)
Period 16-Mar-2017 - 15-Mar-2020
Long-time dynamics of numerical solutions of stochastic differential equations
Mao, Xuerong (Principal Investigator)
Period 01-Oct-2016 - 30-Sep-2021
Doctoral Training Grant 2010 | Craig, Steven
Mao, Xuerong (Principal Investigator)
Period 01-Oct-2010 - 20-Aug-2014
Epsrc Doctoral Training Grant | Liang, Yanfeng
Greenhalgh, David (Principal Investigator) Mao, Xuerong (Co-investigator) Liang, Yanfeng (Research Co-investigator)
Period 01-Oct-2012 - 03-Oct-2016
EPSRC DOCTORAL TRAINING GRANT | Xu, Chang
Mao, Xuerong (Principal Investigator) Xu, Chang (Research Co-investigator)
Period 01-Oct-2011 - 18-May-2017
Industrial Case Account (2008-2012) | Roj, Mikolaj
Higham, Desmond (Principal Investigator) Mao, Xuerong (Co-investigator)
Period 01-Oct-2009 - 10-May-2013

more projects

Address

Mathematics and Statistics
Livingstone Tower

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