Projects per year
Personal profile
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.
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.
Education/Academic qualification
Doctor of Philosophy, University of Warwick
Award Date: 1 Jan 1989
Master of Mathematics, China Textile University
Award Date: 1 Jan 1982
Keywords
- Stochastic differential equations and their applications
- Stochastic analysis
- Numerical analysis of SDEs
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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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Advances in stabilisation of highly nonlinear hybrid delay systems
Dong, H. & Mao, X., 20 Oct 2021, (Accepted/In press) In: Automatica. 11 p.Research output: Contribution to journal › Article › peer-review
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Exponential stabilization by delay feedback control for highly nonlinear hybrid stochastic functional differential equations with infinite delay
Mei, C., Fei, C., Fei, W. & Mao, X., 31 May 2021, In: Nonlinear Analysis: Hybrid Systems. 40, 17 p., 101026.Research output: Contribution to journal › Article › peer-review
1 Citation (Scopus)
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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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.
Xuerong Mao (Keynote/plenary speaker)
23 Apr 2021 → 26 Apr 2021Activity: Participating in or organising an event types › Key-note speaker and plenary lectures at conferences
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The 3nd International Conference on Biomathematical Modelling and Stochastic Analysis, Nanzhou, China, 23-26 April 2021.
Xuerong Mao (Chair)
23 Apr 2021 → 26 Apr 2021Activity: Participating in or organising an event types › Organiser of major conference