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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. 


A note on the partially truncated Euler–Maruyama method
Guo Qian, Liu Wei, Mao Xuerong
Applied Numerical Mathematics Vol 130, pp. 157-170, (2018)
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)
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)
Exponential stability of highly nonlinear neutral pantograph stochastic differential equations
Shen Mingxuan, Fei Weiyin, Mao Xuerong, Deng Shounian
Asian Journal of Control, pp. 1-12, (2018)
Structured robust stability and boundedness of nonlinear hybrid delay systems
Fei Weiyin, Hu Liangjian, Mao Xuerong, Shen Mingxuan
SIAM Journal on Control and Optimization, (2018)
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)

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

Truncated EM method for SDDEs
Invited speaker
The 2018 International Conference on FinTech and Risk Management(FTRM'2018), 19-20 May 2018, Wuhu, China.
Workshop on SDEs and Applications
The IMA Workshop on Ecological and Biological Systems, 4-8 June 2018, Minneapolis,USA.
Invited speaker
Population systems: stochastic vs deterministic
Keynote talk on "Stochastic Modelling in Finance: Motivation, Skills and Applications" at the international Scholars Forum, 28 March 2018, Fuzhou University, China.
Keynote/plenary speaker

more professional activities


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
Mao, Xuerong (Principal 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


Mathematics and Statistics
Livingstone Tower

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