Projects per year
Personal profile
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. 23991 citations, h-index 74, i10-index 209 in Google Scholar on 18 January 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.
Expertise & Capabilities
Stochastic differential equations and their applications.
Education/Academic qualification
Doctor of Philosophy, University of Warwick
Master of Mathematics, China Textile University
Keywords
- Stochastic differential equations and their applications
- Stochastic analysis
- Numerical analysis of SDEs
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Projects
Research Output
Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay
Wang, Y., Wu, F., Mao, X. & Zhu, E., 31 Jan 2020, In : Discrete and Continuous Dynamical Systems - Series B. 25, 1, p. 287-300 14 p.Research output: Contribution to journal › Article
Advances in the truncated Euler-Maruyama method for stochastic differential delay equations
Fei, W., Hu, L., Mao, X. & Xia, D., 30 Apr 2020, In : Communications on Pure and Applied Analysis. 19, 4, p. 2081-2100 20 p.Research output: Contribution to journal › Article
1
Citation
(Scopus)
Datasets
A Stochastic Differential Equation Model for the Spread of HIV Amongst People Who Inject Drugs
Liang, Y. (Creator), Greenhalgh, D. (Creator), Mao, X. (Creator), University of Strathclyde, 2015
DOI: 10.15129/bf5ba8b5-d484-43c7-8006-14fb76819be2
Dataset
Thesis
Convex hulls of planar random walks
Author: Xu, C., 18 May 2017Supervisor: Mao, X. (Supervisor) & Wade, A. (Supervisor)
Student thesis: Doctoral Thesis
Epidemics under environmental noise described by stochastic SIS model
Author: Cai, S., 11 Mar 2020Supervisor: Mao, X. (Supervisor) & Pan, J. (Supervisor)
Student thesis: Doctoral Thesis
Prizes
Activities
Invited talk on "The truncated Euler-Maruyama method for SDDEs" at One World Virtual Seminar Series - Stochastic Numerics and Inverse Problems organised by International Centre for Methematical Sciences (ICMS), Edinburgh, UK, 22 April 2020.
Xuerong Mao (Speaker)2020
Activity: Talk or presentation types › Invited talk
Invited talk 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.
Xuerong Mao (Speaker)2020
Activity: Talk or presentation types › Invited talk