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Professor Xue-Mei Li


  Xue-Mei Lixue-mei-2_-_1.jpg

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 2016/17:
Term 1 MA482 Stochastic Analysis (Handwritten 2016 Notes-1) (Handwritten 2016 Notes-2)(Handwritten 2016 Notes-3) (Exercises) (Solutions)

Term 2: MA3B8 Complex Analysis (Lecture Notes)(Problem Sheets)(Solutions)(Solutions4)(Solutions5)(Solutions6)(solutions7-9)

Research Interests:
Stochastic differential equations and dynamical systems, stochastic analysis on geometric spaces and in infinite dimensions, diffusion processes, investigation of measures, stochastic averagin and homogenization on geometric spaces, investigation of concrete stochastic models.

Research Publications by Topics. Click Here arxiv identifier:

 Most relevant recent publications:

  • Perturbation of Conservation Laws and Averaging on Manifolds (2017), article in arxiv.
  • Doubly Damped Parallel translations and Hessian formulas (2017), submitted to the conference on 'Stochastic Partial Differential Equations and Related Fields'.
  • Generalised Brownian bridges: examples. arxiv:1612.08716 (2016) Markov Processes and Related Fields.
  • Hessian formulas and estimates for parabolic Schrödinger operators. (2016) arxiv:1610.09538 Article
  • Strict Local Martingales: examples. arxiv:1609.00935 article Statistics and Probability Letters (2017).
  • First Order Feynman-Kac Formula. With J. Thompson. (2016) arxiv:1608.03856 Article
  • On the Semi-Classical Brownian Bridge Measure. (2016) arxiv:1607.06498 Article Provisionally Accepted: Electronic Communications in Probability.
  • 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.