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.
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 "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
- Tianyuan Workshop on Stochastic Differential Equations and Related Topics, Shanghai, China, 30 July - 5 August 2022
- Organiser
- 30/7/2022
- 2022 International Symposium on Modelling of Complexity Systems and Intelligent Control, Anhui, China, 23 April 2022.
- Chair
- 23/4/2022
- 2022 International Symposium on Modelling of Complexity Systems and Intelligent Control, Anhui, China, 23 April 2022.
- Keynote/plenary speaker
- 23/4/2022
- Invited talk on "Positivity preserving truncated Euler-Maruyama method for stochastic Lotka-Volterra model Positivity preserving truncated Euler-Maruyama method for stochastic Lotka-Volterra model" at Oxford Stochastic Analysis & Mathematical Finance Seminars on Monday 07/03/2022.
- Invited speaker
- 7/3/2022
- Tianyuan Workshop on Stochastic Differential Equations and Related Topics, Shanghai, China, 30 July - 5 August 2022
- Keynote/plenary speaker
- 2022
More professional activities
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
More projects
Address
Mathematics and Statistics
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