• United Kingdom

1983 …2021
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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


  • Stochastic differential equations and their applications
  • Stochastic analysis
  • Numerical analysis of SDEs

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Euler-Maruyama Method Mathematics

Network Recent external collaboration on country level. Dive into details by clicking on the dots.

Projects 2009 2021

Research Output 1983 2020

Exponential stabilisation of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations

Dong, R., Mao, X. & Birrell, S. A., 2 Jan 2020, (Accepted/In press) In : IET Control Theory and Applications . 11 p.

Research output: Contribution to journalArticle

Open Access
Discrete Time Observations
Exponential Stabilization
Stochastic systems
Periodic Systems
Asymptotic stability

Advances in stabilisation of hybrid stochastic differential equations by delay feedback control

Hu, J., Liu, W., Deng, F. & Mao, X., 27 Dec 2019, (Accepted/In press) In : SIAM Journal on Control and Optimization. 21 p.

Research output: Contribution to journalArticle

Open Access
Feedback Control
Feedback control
Stochastic Equations
Differential equations


Convex hulls of planar random walks

Author: Xu, C., 1 Apr 2015

Supervisor: Mao, X. (Supervisor) & Wade, A. (Supervisor)

Student thesis: Doctoral Thesis

Modelling the effect of stochasticity in epidemic and HIV models

Author: Liang, Y., 1 Apr 2016

Supervisor: Greenhalgh, D. (Supervisor) & Mao, X. (Supervisor)

Student thesis: Doctoral Thesis


Award of Foreign Expert

Xuerong Mao (Recipient), 2014

Prize: Prize (including medals and awards)

Award of Foreign Expert

Xuerong Mao (Recipient), 2011

Prize: Prize (including medals and awards)

Activities 2002 2019