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
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.
Area of Expertise
Stochastic differential equations and their applications.
Prize And Awards
- Medal of 2017 International Scholars' Forum by Shanghai Normal University
- Recipient
- 2017
- Royal Society Wolfson Research Merit Award
- Recipient
- 2016
- Strathclyde Teaching Excellence Award
- Recipient
- 14/5/2015
- The 2013/14 Yangtze River Professorship Award.
- Recipient
- 2015
- The 2015 Leverhulme Research Fellowship Award
- Recipient
- 2015
- Award of Foreign Expert
- Recipient
- 2014
Publications
- An explicit approximation for super-linear stochastic functional differential equations
- Li Xiaoyue, Mao Xuerong, Song Guoting
- Stochastic Processes and their Applications Vol 169 (2024)
- https://doi.org/10.1016/j.spa.2023.104275
- Stationary distribution of periodic stochastic differential equations with Markov switching
- Cai Yongmei, Li Yuyuan, Mao Xuerong
- Journal of Mathematical Analysis and Applications Vol 537 (2024)
- https://doi.org/10.1016/j.jmaa.2024.128291
- On the analysis of Ait-Sahalia-type model for rough volatility modelling
- Coffie Emmanuel, Mao Xuerong, Proske Frank
- Journal of Theoretical Probability Vol 37, pp. 744-767 (2024)
- https://doi.org/10.1007/s10959-023-01269-2
- An advanced numerical scheme for multi-dimensional stochastic Kolmogorov equations with superlinear coefficients
- Cai Yongmei, Mao Xuerong, Wei Fengying
- Journal of Computational and Applied Mathematics Vol 437 (2024)
- https://doi.org/10.1016/j.cam.2023.115472
- Strong convergence of an explicit numerical approximation for n-dimensional superlinear SDEs with positive solutions
- Cai Yongmei, Guo Qian, Mao Xuerong
- Mathematics and Computers in Simulation Vol 216, pp. 198-212 (2024)
- https://doi.org/10.1016/j.matcom.2023.09.011
- 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 (2024)
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
- 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.
- Participant
- 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
- The 4th International Conference on Biomathematical Modelling and Stochastic Analysis, Xuzhou, China, 27 April -1 May 2023.
- Keynote/plenary speaker
- 27/4/2023
- Invited talk on "Advances in nonlinear hybrid SDDEs: existence, boundedness and stability " at the Workshop on Mathematics of Delayed Phenomena, Northumbria University, Newcastle, 22-23 March 2023.
- Invited speaker
- 22/3/2023
- Keynote talk on "Stabilisation in distribution of hybrid ordinary differential equations by periodic noise" at Research Month @FS 2023: Opening Ceremony, University Technology Malaysia, 9 March 2023.
- Keynote/plenary speaker
- 9/3/2023
- Research Month @FS 2023: Opening Ceremony, University Technology Malaysia, 9 March 2023.
- Keynote/plenary speaker
- 9/3/2023
Projects
- 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
- Environment-Ecosystem-Health dynamics under Stochastic Environment
- Mao, Xuerong (Principal Investigator)
- 01-Jan-2014 - 29-Jan-2016
- Workshop on SDDEs
- Mao, Xuerong (Principal Investigator)
- 10-Jan-2013 - 11-Jan-2013