Page personnelle de Shizan FANG







Institut de mathématiques de Bourgogne

    Université de Bourgogne

    9 Avenue Alain Savary

    BP 47870

    Dijon Cedex, France



   Bureau 330, Tél : 03 80 39 58 43

   Membre de l’équipe SPAN




·      (with M. Arnaudon and A.B. Cruzeiro), Generalized stochastic Lagrangian paths for the Navier-Stokes equation, accepted in Annali Scuola Normale sup. di Pisa, 2017.

·      (with D. Luo),  Constantin and Iyer’s  representation formula for the Navier-Stokes equation on manifolds,  Potential Analysis,  2017 (on line).

·      (with B. Wu),  Remarks on spectral gaps on the Riemannian path space, Elec. Comm. Proba.,  22 (2017), no 19, 1-13.

·      (with A. Pilipenko), Additive functional and push forward measures under Veretennikov’s flow, Interdiciplinary Math. Sciences, 17 (2015), 163-178, in honor of Masatoshi Fukushima’s Sansu.

·      (with V. Nolot), Optimal transport maps on infinite dimensional spaces, Front. Math. China, 10 (2015), 715-732.

·      Hydrodynamics and SDE with coefficients in Sobolev space, Modern Stochastics and applications, Springer Optim. Appl. 90 (2014), 109-121.

·      (with V. Nolot) Sobolev estimates for optimal transport maps on Gaussian spaces, Journal of Funct. Analysis, 266 (2014), 5045-5084.

·      (with H. Lee and D. Luo) Heat semi-group and generalized flows on complete Riemannian manifolds, Bull. Sci. Math, 135 (2011), 565-600 (PDF).

·      (with J. Shao) Fokker-Planck equations with respect to heat measures on loop groups, Bull. Sci. Math, 135 (2011), 775-794 (PDF).

·      (with D. Luo and A. Thalmaier) Stochastic differential equations with coefficients in Sobolev spaces, J. Funct. Analysis, 259 (2010), 1129-1168 (PDF).

·      On the behavior of metric Hs on loop groups,  Theory of Stoch. Processes, 16 (2010), 39-43(PDF).

·      (with J. Shao and Th. Sturm) Wasserstein space over the Wiener space, Prob. Theory Related Fields, 146 (2010), 535-565(PDF).

·      (with H. Lee) Commutator estimate for the heat semi-group on compact Riemannian manifolds, Preprint no 569 (2009), IMB.

·      (with J. Shao) Optimal transport maps for Monge-Kantorovich problem on loop groups, J. Funct. Analysis, 248 (2007), 225-257(PDF).


Et Plus





·      Agrégation

·      M4b

·      Mini-cours