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. 23991 citations, h-index 74, i10-index 209 in Google Scholar on 18 January 2020).  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. 


Advances in the truncated Euler-Maruyama method for stochastic differential delay equations
Fei Weiyin, Hu Liangjian, Mao Xuerong, Xia Dengfeng
Communications on Pure and Applied Analysis Vol 19, pp. 2081-2100 (2020)
Exponential stabilisation of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations
Dong Ran, Mao Xuerong, Birrell Stewart A
IET Control Theory and Applications Vol 14, pp. 909-919 (2020)
Stabilisation by delay feedback control for highly nonlinear neutral stochastic differential equations
Shen Mingxuan, Fei Chen, Fei Weiyin, Mao Xuerong
Systems and Control Letters Vol 137 (2020)
The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients
Yang Hao, Wu Fuke, Kloeden Peter E, Mao Xuerong
Journal of Computational and Applied Mathematics Vol 366 (2020)
Stabilisation of highly nonlinear hybrid stochastic differential delay equations by delay feedback control
Li Xiaoyue, Mao Xuerong
Automatica Vol 112 (2020)
Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations
Liu Wei, Mao Xuerong, Tang Jingwen, Wu Yue
Applied Numerical Mathematics Vol 153, pp. 66-81 (2020)

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

Invited talk on "The truncated Euler-Maruyama method for SDDEs" at One World Virtual Seminar Series - Stochastic Numerics and Inverse Problems organised by International Centre for Methematical Sciences (ICMS), Edinburgh, UK, 22 April 2020.
Invited talk on "Advances in stabilisation of hybrid stochastic differential equations by delay feedback control" at One World Virtual Seminar Series - Stochastic Controls organised by Technical Committee on Control Theory (TCCT), Chinese Association of Automation, 20 April 2020.
Chairman and Keynote talk on ”Hybrid SDE models in epidemic systems” at the 2nd International Conference on Biomathematical Modelling and Stochastic Analysis,Huaian, China, 31 October - 3 November 2019.
Keynote talk on ”Stochastic Stability and Stabilisation by Delay Feedback Controls” at the Development Forum 2 - Stochastic Systems and Control during the 38th Chinese Control Conference (CCC2019), Guangzhou, China, 27-30 July 2019.
Keynote talk on "Stochastic Stabilisation by Feedback Controls based on discrete-time observations" at and Chairman of the 2019 TCCT Conference on Stochastic Control, Changchun, China, 15-17 March 2019.
Workshop on SDEs and Application at Strathclyde University, 7-10/08/2019, supported financially by the Royal Society via the Newton Advanced Fellowship.

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)
16-Jan-2017 - 15-Jan-2020
Long-time dynamics of numerical solutions of stochastic differential equations
Mao, Xuerong (Principal Investigator)
01-Jan-2016 - 30-Jan-2021
Numerical Analysis of Stochastic Differential Equations: New Challenges
Mao, Xuerong (Principal Investigator)
01-Jan-2015 - 30-Jan-2017
Environment-Ecosystem-Health dynamics under Stochastic Environment
Mao, Xuerong (Principal Investigator)
01-Jan-2014 - 29-Jan-2016
Workshop on SDDEs
Mao, Xuerong (Principal Investigator)
10-Jan-2013 - 11-Jan-2013
Workshop on Stochastic Differential Equations and Their Applications
Mao, Xuerong (Principal Investigator)
01-Jan-2013 - 30-Jan-2013

more projects


Mathematics and Statistics
Livingstone Tower

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