Quasi-sure flows associated with vector fields of low regularity

Abstract

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.

Keywords

Quasi-sure flows / Abstract Wiener space / Low regularity

References

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