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
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.
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 Sept 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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Collaborations and top research areas from the last five years
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DMS-EPSRC: Stabilization using feedback controls, numerical methods for stochastic systems, and systems with mean-field interactions (EPSRC / NSF scheme)
Mao, X. (Principal Investigator)
EPSRC (Engineering and Physical Sciences Research Council)
1/01/25 → 31/12/27
Project: Research
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ASYMPTOTIC STABILITY OF NEURAL-TYPE STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
Mao, X. (Principal Investigator)
EPSRC (Engineering and Physical Sciences Research Council)
Project: Research
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Stabilisation in distribution of periodic hybrid systems by discrete-time state feedback control
Liu, Z., Hu, J. & Mao, X., 10 Dec 2024, (Accepted/In press) In: SIAM Journal on Control and Optimization.Research output: Contribution to journal › Article › peer-review
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Razumikhin technique for stabilisation of highly nonlinear hybrid systems by bounded discrete-time state feedback control working intermittently
Xu, H. & Mao, X., 1 Dec 2024, In: Numerical Algebra, Control and Optimization. 14, 4, p. 669-687 19 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile66 Downloads (Pure)
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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The 5th International Conference on Bio-mathematical Modelling and Stochastic Analysis, Huaian, China, 18-21 April 2024.
Mao, X. (Chair)
21 Apr 2024 → 24 Apr 2024Activity: Participating in or organising an event types › Organiser of major conference
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Workshop of SDEs and Their Applications, Donghua University, Shanghai, China,18-19 Nov 2023.
Mao, X. (Keynote/plenary speaker)
18 Nov 2023 → 19 Nov 2023Activity: Participating in or organising an event types › Key-note speaker and plenary lectures at conferences