Chinese Annals of Mathematics, Series B

, Volume 35, Issue 1, pp 51–68 | Cite as

Quasi-sure flows associated with vector fields of low regularity

  • Siyan Xu
  • Hua ZhangEmail author


The authors construct a solution U t (x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity, namely one-fold differentiability. Besides, the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained.


Quasi-sure flows Abstract Wiener space Low regularity 

2000 MR Subject Classification

60H07 60H20 60H30 


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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Faculty of SciencesNingbo UniversityNingboZhejiang, China
  2. 2.School of StatisticsJiangxi University of Finance and EconomicsNanchangChina

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