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Stochastic Analysis and Applications Volume 25, 2007 - Issue 5
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Original Articles

Flow of Homeomorphisms and Stochastic Transport Equations

Shizan Fang Institut de Mathématiques, Université de Bourgogne, Dijon, FranceCorrespondence[email protected]
&
Dejun Luo School of Mathematical Sciences, Beijing Normal University, Beijing, China
Pages 1079-1108 | Received 07 Oct 2006, Accepted 19 Apr 2007, Published online: 30 Aug 2007

Citations (18)

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Read on this site (3)

Rongrong Tian, Jinlong Wei & Yanbin Tang. (2020) The second-order parabolic PDEs with singular coefficients and applications. Stochastic Analysis and Applications 38:6, pages 1102-1121.
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Dejun Luo. (2015) Stochastic Lagrangian flows on the group of volume-preserving homeomorphisms of the spheres. Stochastics 87:4, pages 680-701.
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Huaiqian Li & Dejun Luo. (2012) Quasi-Invariant Flow Generated by Stratonovich SDE with BV Drift Coefficient. Stochastic Analysis and Applications 30:2, pages 258-284.
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Articles from other publishers (15)

Vadym Radchenko. (2023) Transport equation driven by a stochastic measure. Modern Stochastics: Theory and Applications, pages 197-209.
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Jinlong Wei, Guangying Lv & Wei Wang. (2022) Stochastic transport equation with bounded and Dini continuous drift. Journal of Differential Equations 323, pages 359-403.
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Jialin Hong & Liying SunJialin Hong & Liying Sun. 2022. Symplectic Integration of Stochastic Hamiltonian Systems. Symplectic Integration of Stochastic Hamiltonian Systems 1 51 .
Jinlong Wei, Jinqiao Duan, Hongjun Gao & Guangying Lv. (2020) Stochastic regularization for transport equations. Stochastics and Partial Differential Equations: Analysis and Computations 9:1, pages 105-141.
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Jie Xu, Jiaping Wen, Jianyong Mu & Jicheng Liu. (2019) Stochastic flows of SDEs with non-Lipschitz coefficients and singular time. Statistics & Probability Letters 148, pages 118-127.
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Dejun Luo. (2014) Quasi-invariance of the Stochastic Flow Associated to Itô’s SDE with Singular Time-Dependent Drift. Journal of Theoretical Probability 28:4, pages 1743-1762.
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Xin Chen & Xue-Mei Li. (2014) Strong completeness for a class of stochastic differential equations with irregular coefficients. Electronic Journal of Probability 19:none.
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Qiao Huijie. (2012) Homeomorphism flows for non-lipschitz SDEs driven by lévy processes. Acta Mathematica Scientia 32:3, pages 1115-1125.
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Dejun Luo. (2010) Pathwise uniqueness of multi-dimensional stochastic differential equations with Hölder diffusion coefficients. Frontiers of Mathematics in China 6:1, pages 129-136.
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Xicheng Zhang. (2010) Stochastic flows and Bismut formulas for stochastic Hamiltonian systems. Stochastic Processes and their Applications 120:10, pages 1929-1949.
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F. Flandoli, M. Gubinelli & E. Priola. (2010) Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift. Bulletin des Sciences Mathématiques 134:4, pages 405-422.
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Xicheng Zhang. (2010) Stochastic flows of SDEs with irregular coefficients and stochastic transport equations. Bulletin des Sciences Mathématiques 134:4, pages 340-378.
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Dejun Luo. (2009) Quasi-invariance of Lebesgue measure under the homeomorphic flow generated by SDE with non-Lipschitz coefficient. Bulletin des Sciences Mathématiques 133:3, pages 205-228.
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Dejun Luo. (2008) Isotropic stochastic flow of homeomorphisms on associated with the critical Sobolev exponent . Stochastic Processes and their Applications 118:8, pages 1463-1488.
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Dejun Luo. (2008) Regularity of solutions to differential equations with non-Lipschitz coefficients. Bulletin des Sciences Mathématiques 132:4, pages 257-271.
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