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 3 in the UK and 75 in the World for Mathematics according to Research.com 2025.
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
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
Recent external collaboration on country/territory level. Dive into details by clicking on the dots or
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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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The asymptotic attraction and stability of hybrid stochastic functional systems with pantograph delay
Mao, W., Jiang, Y., Hu, L. & Mao, X., 1 Nov 2025, (E-pub ahead of print) In: Mathematical Control and Related Files. 19 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile1 Downloads (Pure) -
Stabilization of stochastic functional systems via PI-type controls
Zong, X., Hou, X., Wu, F. & Mao, X., 24 Oct 2025, In: IEEE Control Systems Letters. 9, p. 2429-2434 6 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile1 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 6th International Conference on Biomathematical Modelling and Stochastic Analysis, Zhengzhou, China, 15-18 May 2025.
Mao, X. (Chair)
15 May 2025 → 18 May 2025Activity: Presenting or Organising an Event › Organiser of major conference
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Numerical Algorithms (Journal)
Mao, X. (Editorial board member)
2025 → …Activity: Publication Peer-Review and Editorial Work › Editorial board member