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Geometry on the Wasserstein Space Over a Compact Riemannian Manifold 期刊论文
ACTA MATHEMATICA SCIENTIA, 2021, 卷号: 41, 期号: 6, 页码: 1959-1984
Authors:  Ding, Hao;  Fang, Shizan
Favorite  |  View/Download:38/0  |  Submit date:2022/04/02
constant vector fields  measures having divergence  Levi-Civita connection  parallel translations  Mckean-Vlasov equations  
Constantin and Iyer's Representation Formula for the Navier-Stokes Equations on Manifolds 期刊论文
POTENTIAL ANALYSIS, 2018, 卷号: 48, 期号: 2, 页码: 181-206
Authors:  Fang, Shizan;  Luo, Dejun
Favorite  |  View/Download:116/0  |  Submit date:2018/07/30
Navier-Stokes equations  Stochastic representation  de Rham-Hodge Laplacian  Stochastic flow  Pull-back vector field  
Heat semi-group and generalized flows on complete Riemannian manifolds 期刊论文
BULLETIN DES SCIENCES MATHEMATIQUES, 2011, 卷号: 135, 期号: 6-7, 页码: 565-600
Authors:  Fang, Shizan;  Li, Huaiqian;  Luo, Dejun
Favorite  |  View/Download:75/0  |  Submit date:2018/07/30
Stochastic differential equations with coefficients in Sobolev spaces 期刊论文
JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 卷号: 259, 期号: 5, 页码: 1129-1168
Authors:  Fang, Shizan;  Luo, Dejun;  Thalmaier, Anton
Favorite  |  View/Download:77/0  |  Submit date:2018/07/30
Stochastic flows  Sobolev space coefficients  Density  Density estimate  Pathwise uniqueness  Gaussian measure  Ornstein-Uhlenbeck semigroup  
Transport equations and quasi-invariant flows on the Wiener space 期刊论文
BULLETIN DES SCIENCES MATHEMATIQUES, 2010, 卷号: 134, 期号: 3, 页码: 295-328
Authors:  Fang, Shizan;  Luo, Dejun
Favorite  |  View/Download:148/0  |  Submit date:2018/08/04
Wiener space  Transport equations  Commutator estimate  Quasi-invariant Rows  Malliavin calculus