Projects per year
Personal profile
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.
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.
Expertise & Capabilities
Stochastic differential equations and their applications.
Expertise related to UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This person’s work contributes towards the following SDG(s):
Education/Academic qualification
Doctor of Philosophy, University of Warwick
1 Oct 1987 → 1 Jul 1989
Award Date: 1 Jul 1989
Master of Mathematics, China Textile University
1 Sep 1979 → 31 Aug 1982
Award Date: 31 Aug 1982
Keywords
- Stochastic differential equations and their applications
- Stochastic analysis
- Numerical analysis of SDEs
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Network
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Stochastic Differential Equations: Theory, Numeric and Applications (Saltire Facilitation Award)
1/01/22 → 31/12/23
Project: Knowledge Exchange
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Stochastic stabilization of hybrid neural networks by periodically intermittent control based on discrete-time state observations
Mao, W., You, S., Jiang, Y. & Mao, X., 31 May 2023, In: Nonlinear Analysis: Hybrid Systems. 48, 31 p., 101331.Research output: Contribution to journal › Article › peer-review
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Delay-dependent stability of highly nonlinear neutral stochastic functional differential equations
Shen, M., Fei, C., Fei, W., Mao, X. & Mei, C., 31 Dec 2022, In: International Journal of Robust and Nonlinear Control . 32, 18, p. 9957-9976 20 p.Research output: Contribution to journal › Article › peer-review
Datasets
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A Stochastic Differential Equation Model for the Spread of HIV Amongst People Who Inject Drugs
Liang, Y. (Creator), Greenhalgh, D. (Creator) & Mao, X. (Creator), University of Strathclyde, 2015
DOI: 10.15129/bf5ba8b5-d484-43c7-8006-14fb76819be2
Dataset
Prizes
Activities
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Tianyuan Workshop on Stochastic Differential Equations and Related Topics, Shanghai, China, 30 July - 5 August 2022
Xuerong Mao (Organiser)
30 Jul 2022 → 5 Aug 2022Activity: Participating in or organising an event types › Organiser of major conference
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2022 International Symposium on Modelling of Complexity Systems and Intelligent Control, Anhui, China, 23 April 2022.
Xuerong Mao (Chair)
23 Apr 2022Activity: Participating in or organising an event types › Organiser of major conference