Quasi-sure flows associated with vector fields of low regularity

Chinese Annals of Mathematics, Series B - Tập 35 - Trang 51-68 - 2014
Siyan Xu1, Hua Zhang2
1Faculty of Sciences, Ningbo University, Ningbo, Zhejiang, China
2School of Statistics, Jiangxi University of Finance and Economics, Nanchang, China

Tóm tắt

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.

Tài liệu tham khảo

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