Professor XueMei Li
XueMei LiProfessor Office: C2.10 Phone: +44 (0) 24 76528319 Email: XueMei dot Li at warwick dot ac dot uk

Teaching Responsibilities 2017/18:
None
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 http://arxiv.org/a/li_x_9.
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 SchrÃ¶dinger operators. (2016) arxiv:1610.09538 Article
 Strict Local Martingales: examples. Statistics and Probability Letters 129 (2017) 6568, published version, in arxiv
 First Order FeynmanKac Formula. With J. Thompson. (2016) arxiv:1608.03856 Article Submitted to Stochastic Processes and Their Applications.
 On the SemiClassical Brownian Bridge Measure. (2016) arxiv:1607.06498 Article Electronic Communications in Probability 2017, Vol. 22, paper no. 38, 115
 Reflected Brownian Motion: selection, approximation, and Linearization. With M. Arnaudon arxiv:1602.00897 Article Electronic Journal of Probability 2017, Vol. 22, paper no. 31, 155
 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 166:659712, No 34 (2016). 10.1007/s004400150669x arXiv:1501.04793
 On Hypoelliptic bridge. Aticle Electronic Communications in Probability. Vol 24, no 20, 112 (2016)
 Random Perturbation to the geodesic equation. Article The Annals of Probability, 44(1), 544566, (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 pp134. 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) 151:559590 .
 An approximation scheme for SDEs with nonsmooth coefficients. Xin Chen and XueMei Li (2010). article
 Lack of strong completeness for stochastic flows, XueMei Li and Michael Scheutzow (2011), Ann. of Prob. 2011, Vol. 39, No. 4, 1407–1421 article
 SDE Approach to analysis on path spaces, XueMei Li, In New trends in stochastic analysis and related topics (ed. H. Zhao and A. Truman), World Scientific (2012).
 Intertwined Diffusions by Examples, XueMei 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 XueMei Li. In Frontiers in Mathematics Series, Birkhauser (2010). BookInformation.

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, 398404, World Sci. Publ., Hackensack, NJ, 2010. Article

An L2 theory for differential forms on path spaces I, K. D. Elworthy and XueMei Li . J. Funct. Anal. 254(2008) pp.196245, Article

An averaging principle for Integrable stochastic Hamiltonian systems, XueMei Li. Nonlinearity 21 (2008) pp.803822. Article
Research Grants:
EPSRC research grant on Stochastic Analysis in Infinite Dimensional Spaces, 20082011.
LMS scheme three grant (East Midland Stochastic Analysis Seminars), 20022016.