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Professor Xue-Mei Li



Xue-Mei Li


Office: C2.10

Phone: +44 (0) 24 76528319

Email: Xue-Mei dot Li at warwick dot ac dot uk

Personal Home Page


Teaching Responsibilities 2017/18:

Research Interests:
I am curently working on perturbation to conservation laws related to group actions, stochastic averaging, diffusion creation of stochastic differential equations on manifolds. I am also working on Hessian estimates of parabolic second order differential equations. Otherwise I work with stochastic dynamical systems, stochastic analysis on geometric spaces and in infinite dimensions, geometry of diffusion processes, investigation of measures and concrete stochastic models.

To see a list of my research publications, organised by topics, pelase Click Here. For my articles in the arxiv, use

 Most relevant recent publications:

  • Perturbation of Conservation Laws and Averaging on Manifolds (2017), article in arxiv, submitted to Abelsymposium 2016.
  • Doubly Damped Parallel translations and Hessian formulas (2017), To appear in the volume 'Stochastic Partial Differential Equations and Related Fields', on the occasion of Michale Roeckner's 60th birthday.
  • Generalised Brownian bridges: examples. arxiv:1612.08716 (2016) Submitted to Markov Processes and Related Fields.
  • Hessian formulas and estimates for parabolic Schrödinger operators. (2016) arxiv:1610.09538 Article
  • Strict Local Martingales: examples. Statistics and Probability Letters 129 (2017) 65-68, published version, in arxiv
  • First Order Feynman-Kac Formula. With J. Thompson. (2016) arxiv:1608.03856 Article To appear: Stochastic Processes and Their Applications.
  • On the Semi-Classical Brownian Bridge Measure. (2016) arxiv:1607.06498 Article Electronic Communications in Probability 2017, Vol. 22, paper no. 38, 1-15
  • Reflected Brownian Motion: selection, approximation, and Linearization. With M. Arnaudon arxiv:1602.00897 Article Electronic Journal of Probability 2017, Vol. 22, paper no. 31, 1-55
  • Stochastic Homogenisation on Homogeneous Spaces (with an appendix by D. Rumynin) (2016) Article arXiv:1505.06772. To appear: Journal of the Mathematical Society of Japan.
  • Limits of Random Differential Equations on Manifolds. Article. Probability Theory Related Fields. Vol 166:659-712, No 3-4 (2016). 10.1007/s00440-015-0669-x arXiv:1501.04793
  • On Hypoelliptic bridge. Aticle Electronic Communications in Probability. Vol 24, no 20, 1-12 (2016)
  • Random Perturbation to the geodesic equation. Article The Annals of Probability, 44(1), 544-566, (2016). arxiv:1402.5861
  • Strong completeness for a class of stochastic differential equations with irregular coefficients, X. Chen and X.-M. Li Article, Electronic Journal of Probability, 19 (2014), no. 91 pp1-34. arXiv:1402.5079
  • Effective Diffusions with Intertwined Structures (2012) Article Arxiv:1204.3250
  • A Concrete Estimate For The Weak Poincare Inequality On Loop Space. X. Chen, X.-M. Li and B. Wu. Article Probab. Theory Relat. Fields (2011) 151:559-590 .
  • An approximation scheme for SDEs with non-smooth coefficients. Xin Chen and Xue-Mei Li (2010). article
  • Lack of strong completeness for stochastic flows, Xue-Mei Li and Michael Scheutzow (2011), Ann. of Prob. 2011, Vol. 39, No. 4, 1407–1421 article
  • SDE Approach to analysis on path spaces, Xue-Mei Li, In New trends in stochastic analysis and related topics (ed. H. Zhao and A. Truman), World Scientific (2012).
  • Intertwined Diffusions by Examples, Xue-Mei Li (2010). In Stochastic Analysis 2010; Springer. ed. D. Crisan. Article 
  • A Poincare Inequality on Loop spaces, X. Chen, X.-M. Li and B. Wu. J. Funct. Anal., vol. 259 (2010). Article
  • The Geometry of Filtering, K. D. Elworthy, Yves Le Jan, and Xue-Mei Li. In Frontiers in Mathematics Series, Birkhauser (2010). Book-Information.
  • A Spectral Gap for the Brownian Bridge measure on hyperbolic spaces. X. Chen, X.-M. Li and B. Wu. Progress in analysis and its applications, 398-404, World Sci. Publ., Hackensack, NJ, 2010. Article
  • An L2 theory for differential forms on path spaces I, K. D. Elworthy and Xue-Mei Li . J. Funct. Anal. 254(2008) pp.196--245, Article
  • An averaging principle for Integrable stochastic Hamiltonian systems, Xue-Mei Li. Nonlinearity 21 (2008) pp.803--822. Article

Research Grants:

EPSRC research grant on Stochastic Analysis in Infinite Dimensional Spaces, 2008-2011.

LMS scheme three grant (East Midland Stochastic Analysis Seminars), 2002-2016.