Preprints and publications

Xue-Mei Li

 

    Preprints

    • Strong completeness of SDEs and non-explosion for RDEs with coefficients having unbounded derivatives (2025) arxiv article.
    • Scaling limit of the KPZ equation with non-integrable spatial correlations(2024) arxiv article
    • Fluctuations of stochastic PDEs with long-range correlations (2024) arxiv article
    • Coarse Ricci curvature of weighted Riemannian manifolds (2023) arxiv article
    • Diffusive and rough homogenisation in fractional noise field(2020), article.
    • Homogenization with fractional random fields(2019), article.

    Publications

  • Coarse extrinsic curvature of Riemannian submanifolds (2024) To appear: European J. of Mathematics arxiv article
  • Logarithmic heat kernels estimates without curvature restrictions Ann. Probab. 51(6): 2056-2085 (November 2023). DOI: 10.1214/23-AOP1638 arxiv article; on journal site
  • On the (Non-)Stationary Density of Fractional-Driven Stochastic Differential Equations Ann. Probab. 51(6): 2056-2085 (November 2023). DOI: 10.1214/23-AOP1638 arxiv article; on journal site
  • Log-Hessian formula and the Talagrand conjecture. Potential Analysis, Volume 58, pages 123-158, (2023) article on arxiv;. on journal site
  • Effective Diffusions with Intertwined Structures; Matemática Contemporânea 2023, vol. 58 Click for article Arxiv:1204.3250,
  • Functional Limit Theorems for Volterra Processes and Applications to Homogenization (2021), Nonlinearity Vol 35 1521, 2022. Article on journal site; article on arxiv.
  • Generating Diffusions with Fractional Brownian Motion (2022), Communications in Mathematical Physics, Volume 396, pages 91-141, (2022) Article on journal site; article on arxiv.
  • Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging (2021), Stochastics and Dynamics, Vol. 22, No. 07, 2240025, Best Paper Award (2022) Article on journal site; article on arxiv.
  • Rough Homogenisation with Fractional Dynamics, Published in "Geometry and Invariance in Stochastic Dynamics (Verona, Italy, March 25-29, 2019)", eds: Editors: Stefania Ugolini, Marco Fuhrman, Elisa Mastrogiacomo, Paola Morando, Barbara Ruediger; pp 137--168, 2022 article; on journal site; arxiv 2011.00075
  • Slow-Fast Systems with Fractional Environment and Dynamics Ann. Appl. Probab. 32(5): 3964-4003 (October 2022). DOI: 10.1214/22-AAP1779 Article on Arxiv
  • Functional limit theorems for the fractional Ornstein-Uhlenbeck process article. In Journal of Theoretical Probability, 35(1), pp 426-456, 2022. access to journal article
  • Hessian formulas and estimates for parabolic Schroedinger operators , Journal of Stochastic Analysis, 2(3), 2021, on journal site; on Arxiv
  • Averaging dynamics driven by fractional Brownian motion Ann. Probab. 48(4): 1826-1860 (July 2020). DOI: 10.1214/19-AOP1408 click for article omn journal site. click for article on arxiv.
  • Generalised Brownian bridges: examples . In "Markov Processes and Related Fields"", 2018, v.24, Issue 1, 151-163. Arxiv article
  • Homogenisation on Homogeneous Spaces (with an appendix by D. Rumynin) (2018) Article In Journal of the Mathematical Society of Japan, article on journal site
  • Perturbation of Conservation Laws and Averaging on Manifolds (2017), article. In Abelsymposium 2016.
  • Doubly Damped Parallel translations and Hessian formulas , In `Stochastic Partial Differential Equations and Related Fields'', `in Honor of Michael Roeckner, SPDERF, Bielefeld, Germany, October 10-14, 2016', Springer Proceedings in Mathematics & Statistics, (2018) Click here for article on journal site, Click here for article on Arxiv
  • First order Feynman-Kac Formula. In Stochastic Processes and their applications, Volume 128, Issue 9, September 2018, Pages 3006-3029, doi.org/10.1016/j.spa.2017.10.010. on arxiv; article on journal site
  • Reflected Brownian Motion: selection, approximation, and Linearization. arxiv:1602.00897 Article  Electronic Journal of Probability 2017, Vol. 22, paper no. 31, 1-55
  • On the Semi-Classical Brownian Bridge Measure arxiv:1607.06498 Article Electronic Communications in Probability 2017, Vol. 22, paper no. 38, 1-15
  • Strict Local Martingales: examples. Statistics and Probability Letters 129(2017) 65-68. published version arxiv:1609.00935 Article in Arxiv .
  • 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
  • Random Perturbation to the geodesic equation The Annals of Probability , 44(1), 544-566, (2016), arxiv:1402.5861 article on journal site; Click for article on arxiv
  • On Hypoelliptic bridge. Aticle  Electronic Communications in Probability; Vol 24, no 20, 1-12 (2016)
  • Strong completeness for a class of stochastic differential equations with irregular coefficients Electronic J. of Probability. 19 (2014) no. 91 1-34. article. also in arXiv:1402.5079
  • The stochastic differential equation approach to analysis on path space . In New trends in stochastic analysis and related topics, 207-226, (2012) click for article
  • Lack of strong completeness for stochastic flows , Annals of Probability, vol 39(4), 1407-1421 (2011). article
  • A Concrete Estimate For The Weak Poincare Inequality On Loop Space . Probab. Theory Relat. Fields (2011) 151:559-590   article
  • A spectral gap for the Brownian bridge measure on hyperbolic spaces In Progress in analysis and its applications, 398-404, World Sci. Publ., Hackensack, NJ, 2010. article  
  • A Poincare Inequality on Loop spaces, J. of Functional Analysis. vol 259 (6), pp 1421-1442 (2010)   article
  • Intertwined Diffusions by Examples. In `Stochastic Analysis 2010', Springer. ed. D. Crisan. (2010) article article on journal site
  • An averaging principle for Integrable stochastic Hamiltonian systems Nonlinearity 21 (2008) pp.803--822,   Article on arxiv; Article on Journal site
  • An L2 theory for differential forms on path spaces I , J. Funct. Anal. 254(2008) pp.196--245   article
  • Itô maps and analysis on path spaces. Math. Zeitschrift. (2007) 257: pp 643--706.   article
  • Geometric stochastic analysis on path spaces, > In Proceedings of the International Congress of Mathematicians Madrid, August 22-30, 2006, Volume III. Invited Lectures, pp575--594 article on arxiv; article on journal site
  • Intertwining and the Markov uniqueness problem on path spaces, In Stochastic Partial Differential Equations and Applications - VII, eds G. Da Prato, L. Tubaro. (2006). article
  • Barycentres of probability measures transported by stochastic flows . Annals of Probability, vol 33, No.4, 1509-1543. (2025). Article on journal site; on arxiv
  • Equi-variant Diffusions on Principal Bundles In "Stochastic Analysis and Related Topics in Kyoto: In honour of Kiyosi Itô", Editor(s) Hiroshi Kunita, Shinzo Watanabe, Yoichiro Takahashi Adv. Stud. Pure Math., 41: 373pp. (2004). DOI: 10.2969/aspm/04110000 on arviv, On journal site; article
  • Gross-Sobolev spaces on path manifolds: uniqueness and intertwining by Itô maps. C. R. Acad. Sci. Paris, Ser. I 337 (2003) 741-744.
  • Some Families of q-vector fields on path spaces article Infinite Dimensional Analysis, Quantum Probability and Related Topics. Volume 6, pages 1-27 (2003).
  • On compactness of manifolds and existence of certain type functional inequalities Infinite Dimensional Analysis, Quantum Probability and Related Topics. Volume 6, pages 29-38, (2003) article; on journal site
  • Large time asymptotics of Barycentres of Brownian motions on Hyperbolic spaces In Analyse Stochastique et Theorie du Potential. (2003) article
  • Hodge de Rham decomposition for an L2 space of differential 2-forms on path spaces Abstracts of International Conference on Stochastic Analysis and Related Topics, St Petersburg, Russia (2002). article
  • Special Itô maps and an L2 Hodge theory for one forms on path spaces, Stochastic Processes, Physics and Geometry: New Interplays. II: A Volume in Honor of Sergio Albeverio Edited by: Fritz Gesztesy, Helge Holden,Jürgen Jost,Sylvie Paycha,Michael Röckner, Sergio Scarlatti. CMS Conf. Proc., 28, Amer. Math. Soc., Providence, RI, 2000. article; ams site
  • Manifold-valued martingales, change of probabilities, and smoothness of finely harmonic maps . Annals of Institute Henri Poincare. Vol. 35, no. 6, p.765-791. article; journal site (1999)
  • The importance of strictly local martingales, applications to Ornstein-Uhlenbeck processes Probab. Theory and Relat. Fields. vol 115. p.325-355. (1999). article; journal site
  • Bounded and L^2 Harmonic Forms on Universal Covers .    Geom.  And Funct. Anal. Vol. 8 , 283-303 (1998). article; journal site
  • Bismut type formula for differential forms . C. R. Acad. Sci. t. 327, Série I, 87-92, (1998) article
  • On the tails of the supremum and the quadratic variation of strictly local martingales .   Sem. prob. XXXI, LNM 1655, June 1997. article on Numdam
  • Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups. C. R. Acad. Sci. t.323 série 1, p. 921-926 (1997). article
  • Concerning the geometry of stochastic differential equations and stochastic flows .  In 'New Trends in Stochastic Analysis', Proc. Taniguchi Symposium, Sept. 1995, Charingworth, ed. K. D. Elworthy and S. Kusuoka, I. Shigekawa, World Scientific Press. (1997). article on arxiv
  • Gradient estimates and the smooth convergence of approximate travelling waves for reaction-diffusion equations. Nonlinearity, 9, 459-477 (1996) article; on journal site
  • A class of Integration by parts formulae in stochastic analysis I . Itô's Stochastic Calculus and Probability Theory (dedicated to Itô on the occasion of his eightieth birthday) , ed. S. Watanabe. Springer, (1996). article; on journal site
  • On extensions of Myers' theorem,   Bull. London Math. Soc. 27, 392-396. 1995. article; on journal site
  • Derivative flows of stochastic differential equations: moment exponents and geometric properties. Stochastic Analysis. In AMS Proceedings of Symposia in Pure Mathematics. Eds. Cranston, M. G. and Pinsky, M. A. p. 565-574. 1995. article; on ams site
  • Formulae for the derivatives of heat semigroups . J. Funct. Anal. 125, 1, 252-286. 1994.   article;   on journal site; on arxiv
  • Differentiation of heat semigroups and applications. Probability Theory and Mathematics Stats (Proc. 6th Vilnius conferences). Eds. B. Grigelionis et al. VSP/TEV, Utrecht and Vilnius. In New Titles in Probability and Statistics Series. p. 239-251. 1994.   article
  • Stochastic differential equations on non-compact manifolds: moment stability and its topological consequences ,   Probab. Theory Relat. Fields. 100, 4, 417-428. 1994. article;  on arxiv; on journal site
  • Strong p-completeness of stochastic differential equations and the existence of smooth flows on non-compact manifolds .  Probab. Theory Relat. Fields. 100, 4, 485-511. 1994, article;     on journal site;  on arxiv;  
  • Properties at infinity of diffusion semigroups and stochastic flows via weak uniform cover; In Potential Analysis Published: December 1994 Volume 3, pages 339–357, article   on journal site  on arxiv site 
  • Curvature and topology: spectral positivity.  Methods and Applications of Global Analysis, Ed. Yu Gliklikh. In Voronezh Series on New Developments in Global Analysis.p. 45-60. 1993. article
  • Stochastic Flows on Noncompact Manifolds. Ph.D. thesis (1992).
  • Behaviour at infinity of stochastic solutions and diffusion semi-groups . M.Sc. Dissertation (1989).

    • Research Books

  • On the Geometry of Diffusion Operators and Stochastic Flows . Lecture Notes in Mathematics, volume 1720, Springer-Verlag (1999). Introduction click for book
  • The Geometry of Filtering, click here for book Birkhauser, (2010)

    • Other Preprints

  • An approximation scheme for SDEs with non-smooth coefficients. (2010) article