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.
Professional activities
- The 3nd International Conference on Biomathematical Modelling and Stochastic Analysis, Nanzhou, China, 23-26 April 2021.
- Chair
- 23/4/2021
- 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.
- Keynote/plenary speaker
- 23/4/2021
- Keynote talk (via Zoom) on "Stochastic stabilization by feedback controls based on discrete-time observations: past, present and future" at the Salong on Stochastic Systems and Controls on 26 Dec 2020 organised by Science China Press.
- Keynote/plenary speaker
- 26/12/2020
- Keynote talk (via Zoom) on "Stabilisation of highly nonlinear hybrid SDDEs by delay feedback controls" at the 8th TCCT Conference on Stochastic Systems and Controls, Liaocheng, China, 23-25 October 2020.
- Keynote/plenary speaker
- 23/10/2020
- Invited talk (via Zoom) on "The truncated Euler-Maruyama method for SDDEs" at One World Virtual Seminar Series - Stochastic Numerics and Inverse Problems organised by International Centre for Mathematical Sciences (ICMS), Edinburgh, UK, 22 April 2020.
- Invited speaker
- 22/4/2020
- Invited talk (via Zoom) on "Advances in stabilisation of hybrid stochastic differential equations by delay feedback control" at One World Virtual Seminar Series - Stochastic Controls organised by Technical Committee on Control Theory (TCCT), Chinese Association of Automation, 20 April 2020.
- Invited speaker
- 20/4/2020
More professional activities
Projects
- 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
- Workshop on Stochastic Differential Equations and Their Applications
- Mao, Xuerong (Principal Investigator)
- 01-Jan-2013 - 30-Jan-2013
More projects
Address
Mathematics and Statistics
Livingstone Tower
Livingstone Tower
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