Professor Xuerong Mao
Mathematics and Statistics
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.
Area of Expertise
Stochastic differential equations and their applications.
Prize And Awards
- Award of Highly Ranked Scholar - Lifetime by ScholarGPS 2025
- Recipient
- 2025
- Strathclyde Teaching Excellent Award 2024: Winner of Most Memorable Category.
- Recipient
- 2024
- Research.com Mathematics in United Kingdom Leader Award 2024: ranked #95 in the world ranking and #5 in United Kingdom.
- Recipient
- 2024
- Award of Highly Ranked Scholar - Lifetime by ScholarGPS 2024
- Recipient
- 2024
- Research.com Mathematics in United Kingdom Leader Award 2023: ranked #86 in the world ranking and #4 in United Kingdom.
- Recipient
- 2023
- Research.com Mathematics in United Kingdom Leader Award 2022: ranked #95 in the world ranking and #1 in United Kingdom.
- Recipient
- 2022
Publications
- Stabilization in distribution of periodic hybrid systems by discrete-time state feedback control
- Liu Zhijun, Hu Junhao, Mao Xuerong
- SIAM Journal on Control and Optimization Vol 63, pp. 1243-1266 (2025)
- https://doi.org/10.1137/24M1655627
- Explicit multiscale numerical method for super-linear slow-fast stochastic differential equations
- Cui Yuanping, Li Xiaoyue, Mao Xuerong
- Stochastic Processes and their Applications (2025)
- https://doi.org/10.1016/j.spa.2025.104653
- On the decay rate for a stochastic delay differential equation with an unbounded delay
- Yao Xin, You Surong, Mao Wei, Mao Xuerong
- Applied Mathematics Letters Vol 166 (2025)
- https://doi.org/10.1016/j.aml.2025.109541
- Stationary distribution and extinction of an HCV transmission model with protection awareness and environmental fluctuations
- Wang Liangwei, Wei Fengying, Jin Zhen, Mao Xuerong
- Applied Mathematics Letters Vol 160 (2025)
- https://doi.org/10.1016/j.aml.2024.109356
- HCV transmission model with protection awareness in an SEACTR community
- Wang Liangwei, Wei Fengying, Jin Zhen, Mao Xuerong, Cai Shaojian, Chen Guangmin, Zheng Kuicheng, Xie Jianfeng
- Infectious Disease Modelling Vol 10, pp. 559-570 (2025)
- https://doi.org/10.1016/j.idm.2024.12.014
- Stabilization of hybrid stochastic differential equations by delay feedback control based on discrete-time observations
- Chen Xing, Li Xiaoyue, Mao Xuerong
- Numerical Algebra, Control and Optimization Vol 14, pp. 706-723 (2024)
- https://doi.org/10.3934/naco.2024009
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
- Chairman of the 4th International Conference on Biomathematical Modelling and Stochastic Analysis, Xuzhou, China, 27 April -1 May 2023.
- Organiser
- 27/4/2023
Projects
- Stabilization of Hybrid Stochastic Differential Equations by Discrete-Time-State-Feedback Control
- Mao, Xuerong (Principal Investigator)
- 02-Jan-2025 - 09-Jan-2025
- DMS-EPSRC: Stabilization using feedback controls, numerical methods for stochastic systems, and systems with mean-field interactions (EPSRC / NSF scheme)
- Mao, Xuerong (Principal Investigator)
- 01-Jan-2025 - 31-Jan-2027
- 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