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 (e.g. 18853 citations, h-index 66, i10-index 182 in Google Scholar on 19/12/2017). 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
- Workshop on SDEs and Applications
- Organiser
- 2018
- The IMA Workshop on Ecological and Biological Systems, 4-8 June 2018, Minneapolis,USA.
- Invited speaker
- 2018
- Keynote talk on "Stochastic Modelling in Finance: Motivation, Skills and Applications" at the international Scholars Forum, 28 March 2018, Fuzhou University, China.
- Keynote/plenary speaker
- 2018
- The 2018 International Conference on FinTech and Risk Management（FTRM'2018）, 19-20 May 2018, Wuhu, China.
- Chair
- 2018
- Population systems: stochastic vs deterministic
- Speaker
- 2018
- Truncated EM method for SDDEs
- Invited speaker
- 2018
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)
- Period 16-Mar-2017 - 15-Mar-2020
- Long-time dynamics of numerical solutions of stochastic differential equations
- Mao, Xuerong (Principal Investigator)
- Period 01-Oct-2016 - 30-Sep-2021
- Doctoral Training Grant 2010 | Craig, Steven
- Mao, Xuerong (Principal Investigator)
- Period 01-Oct-2010 - 20-Aug-2014
- Epsrc Doctoral Training Grant | Liang, Yanfeng
- Greenhalgh, David (Principal Investigator) Mao, Xuerong (Co-investigator) Liang, Yanfeng (Research Co-investigator)
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- Period 01-Oct-2012 - 03-Oct-2016
- EPSRC DOCTORAL TRAINING GRANT | Xu, Chang
- Mao, Xuerong (Principal Investigator)
- Period 01-Oct-2011 - 18-May-2017
- Industrial Case Account (2008-2012) | Roj, Mikolaj
- Higham, Desmond (Principal Investigator) Mao, Xuerong (Co-investigator)
- Period 01-Oct-2009 - 10-May-2013
more projects
Address
Mathematics and Statistics
Livingstone Tower
Livingstone Tower
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