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.  He is a Highly Cited Researchers 2020 in the file of mathematics (Clarivate):

https://recognition.webofscience.com/awards/highly-cited/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. 

Publications

Feedback delay control of highly nonlinear stochastic functional differential equations with discrete-time state observations
Mei Chunhui, Liang Yong, Fei Weiyin, Mao Xuerong
Mathematical Methods in the Applied Sciences (2021)
Exponential stabilization by delay feedback control for highly nonlinear hybrid stochastic functional differential equations with infinite delay
Mei Chunhui, Fei Chen, Fei Weiyin, Mao Xuerong
Nonlinear Analysis: Hybrid Systems Vol 40 (2021)
https://doi.org/10.1016/j.nahs.2021.101026
Stabilisation in distribution by delay feedback control for hybrid stochastic differential equations
You Surong, Hu Liangjian, Lu Jianqiu, Mao Xuerong
IEEE Transactions on Automatic Control (2021)
https://doi.org/10.1109/TAC.2021.3075177
Strong convergence and asymptotic stability of explicit numerical schemes for nonlinear stochastic differential equations
Li Xiaoyue, Mao Xuerong, Yang Hongfu
Mathematics of Computation (2021)
https://doi.org/10.1090/mcom/3661
Stabilization of hybrid systems by intermittent feedback controls based on discrete-time observations with a time delay
Jiang Yanan, Hu Liangjian, Lu Jianqiu, Mao Wei, Mao Xuerong
IET Control Theory and Applications (2021)
Stabilization and destabilization of hybrid systems by periodic stochastic controls
Li Xiaoyue, Liu Wei, Mao Xuerong, Zhao Junsheng
Systems and Control Letters (2021)

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

The 3nd International Conference on Biomathematical Modelling and Stochastic Analysis, Nanzhou, China, 23-26 April 2021.
Chair
23/4/2021
Chairman and keynote talk on "Monte Carlo simulations of SDE models" at the 3nd International Conference on Biomathematical Modelling and Stochastic Analysis, Nanzhou, China, 23-26 April 2021.
Keynote/plenary speaker
23/4/2021
Keynote talk (via Zoom) on "Stochastic stabilization by feedback controls based on discrete-time observations: past, present and future" at the Salong on Stochastic Systems and Controls on 26 Dec 2020 organised by Science China Press.
Keynote/plenary speaker
26/12/2020
Keynote talk (via Zoom) on "Stabilisation of highly nonlinear hybrid SDDEs by delay feedback controls" at the 8th TCCT Conference on Stochastic Systems and Controls, Liaocheng, China, 23-25 October 2020.
Keynote/plenary speaker
23/10/2020
Invited talk (via Zoom) on "The truncated Euler-Maruyama method for SDDEs" at One World Virtual Seminar Series - Stochastic Numerics and Inverse Problems organised by International Centre for Mathematical Sciences (ICMS), Edinburgh, UK, 22 April 2020.
Invited speaker
22/4/2020
Invited talk (via Zoom) 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.
Invited speaker
20/4/2020

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)
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

Address

Mathematics and Statistics
Livingstone Tower

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