Professor Xuerong Mao

Mathematics and Statistics

Personal statement

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

He is a very active and extremely highly cited stochastic analyst.  He is among the top list of Best Mathematics Scientists in United Kingdom:

https://research.com/scientists-rankings/mathematics/gb

placed number 1 in the UK and 93 in the World for Mathematics according to Research.com.

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 backward Euler-Maruyama method for invariant measures of stochastic differential equations with super-linear coefficients
Liu Wei, Mao Xuerong, Wu Yue
Applied Numerical Mathematics Vol 184, pp. 137-150 (2023)
https://doi.org/10.1016/j.apnum.2022.09.017
Asymptotic stability in distribution of highly nonlinear stochastic differential equations with G-Brownian motion
Fei Chen, Fei Weiyin, Deng Shounian, Mao Xuerong
Qualitative Theory of Dynamical Systems Vol 22 (2023)
Dynamics of an HIV/AIDS transmission model with protection awareness and fluctuations
Zhai Xuanpei, Li Wenshuang, Wei Fengying, Mao Xuerong
Chaos, Solitons and Fractals Vol 169 (2023)
https://doi.org/10.1016/j.chaos.2023.113224
A note on sufficient conditions of asymptotic stability in distribution of stochastic differential equations with G-Brownian motion
Fei Chen, Fei Weiyin, Mao Xuerong
Applied Mathematics Letters Vol 136 (2023)
https://doi.org/10.1016/j.aml.2022.108448
Advances in nonlinear hybrid stochastic differential delay equations : existence, boundedness and stability
Hu Junhao, Mao Wei, Mao Xuerong
Automatica Vol 147 (2023)
https://doi.org/10.1016/j.automatica.2022.110682
Stochastic stabilization of hybrid neural networks by periodically intermittent control based on discrete-time state observations
Mao Wei, You Surong, Jiang Yanan, Mao Xuerong
Nonlinear Analysis: Hybrid Systems Vol 48 (2023)
https://doi.org/10.1016/j.nahs.2023.101331

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

Keynote talk on "Stabilisation in distribution of hybrid ordinary differential equations by periodic noise" at Research Month @FS 2023: Opening Ceremony, University Technology Malaysia, 9 March 2023.
Keynote/plenary speaker
9/3/2023
Tianyuan Workshop on Stochastic Differential Equations and Related Topics, Shanghai, China, 30 July - 5 August 2022
Organiser
30/7/2022
2022 International Symposium on Modelling of Complexity Systems and Intelligent Control, Anhui, China, 23 April 2022.
Chair
23/4/2022
2022 International Symposium on Modelling of Complexity Systems and Intelligent Control, Anhui, China, 23 April 2022.
Keynote/plenary speaker
23/4/2022
Invited talk on "Positivity preserving truncated Euler-Maruyama method for stochastic Lotka-Volterra model Positivity preserving truncated Euler-Maruyama method for stochastic Lotka-Volterra model" at Oxford Stochastic Analysis & Mathematical Finance Seminars on Monday 07/03/2022.
Invited speaker
7/3/2022
Tianyuan Workshop on Stochastic Differential Equations and Related Topics, Shanghai, China, 30 July - 5 August 2022
Keynote/plenary speaker
2022

More professional activities

Projects

Stochastic Differential Equations: Theory, Numeric and Applications (Saltire Facilitation Award)
Mao, Xuerong (Principal Investigator)
01-Jan-2022 - 31-Jan-2023
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

More projects

Address

Mathematics and Statistics
Livingstone Tower

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