Professor Xuerong Mao

Mathematics and Statistics

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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

ranked number 5 in the UK and 95 in the World for Mathematics according to Research.com 2024.

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. 

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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 5th International Conference on Bio-mathematical Modelling and Stochastic Analysis, Huaian, China, 18-21 April 2024.
Chair
21/4/2024
Workshop of SDEs and Their Applications, Donghua University, Shanghai, China,18-19 Nov 2023.
Keynote/plenary speaker
18/11/2023
International Symposium on Stochastic Systems Theory and Intelligent Control, Wuhu, Anhui, China, 1-4 August 2023.
Keynote/plenary speaker
1/8/2023
International Conference on Bio-mathematical and Dynamical Systems, Enshi, China, 9-12 July 2023.
Keynote/plenary speaker
9/7/2023
Keynote talk on "Advances in nonlinear hybrid SDDEs: Existence, Boundedness and Stability" at the 10th TCCT Conference on Stochastic Systems and Controls, Wuhan, China, 4-7 May 2023.
Keynote/plenary speaker
4/5/2023
The 4th International Conference on Biomathematical Modelling and Stochastic Analysis, Xuzhou, China, 27 April -1 May 2023.
Keynote/plenary speaker
27/4/2023

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

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Contact

Professor Xuerong Mao
Mathematics and Statistics

Email: x.mao@strath.ac.uk
Tel: 548 3669