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. 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.
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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Network
Recent external collaboration on country level. Dive into details by clicking on the dots.
Projects 2009 2021
Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)
16/03/17 → 15/03/20
Project: Research Fellowship
Long-time dynamics of numerical solutions of stochastic differential equations
1/10/16 → 30/09/21
Project: Research
Research Output 1983 2020
Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay
Wang, Y., Wu, F., Mao, X. & Zhu, E., 18 Mar 2019, (Accepted/In press) In : Discrete and Continuous Dynamical Systems - Series B. 14 p.Research output: Contribution to journal › Article
Stochastic Functional Differential Equations
Infinite Delay
Differential equations
Theorem
Lyapunov functions
Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching
Mao, W., Hu, L. & Mao, X., 5 Aug 2019, In : Electronic Journal of Qualitative Theory of Differential Equations. 52, p. 1-17 17 p.Research output: Contribution to journal › Article
Open Access
File
Almost Sure Stability
Pantograph Equation
Pantographs
Markovian Switching
Decay Rate
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., 1 Apr 2015Supervisor: Mao, X. (Supervisor) & (Supervisor)
Student thesis: Doctoral Thesis
Modelling the effect of stochasticity in epidemic and HIV models
Author: Liang, Y., 1 Apr 2016Supervisor: Greenhalgh, D. (Supervisor) & Mao, X. (Supervisor)
Student thesis: Doctoral Thesis
Prizes
Activities 2002 2019
Keynote talk on ”Stochastic Stability and Stabilisation by Delay Feedback Controls” at the Development Forum 2 - Stochastic Systems and Control during the 38th Chinese Control Conference (CCC2019), Guangzhou, China, 27-30 July 2019.
Xuerong Mao (Participant)2019
Activity: Participating in or organising an event types › Key-note speaker and plenary lectures at conferences
Keynote talk on "Stochastic Stabilisation by Feedback Controls based on discrete-time observations" at and Chairman of the 2019 TCCT Conference on Stochastic Control, Changchun, China, 15-17 March 2019.
Xuerong Mao (Participant)2019
Activity: Participating in or organising an event types › Key-note speaker and plenary lectures at conferences