Quasi-sure flows associated with vector fields of low regularity
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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.
KeywordsQuasi-sure flows Abstract Wiener space Low regularity
2000 MR Subject Classification60H07 60H20 60H30
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