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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
This paper consideres the existence of flows associated with vector fields under low regularity. Using the finite dimensional approximations of vector fields and a capacity version of Kolmogorov’s criterion for path continuity, and the existence of almost-sure flows of vector fields, the authors construct (1,p)-quasi-sure flows for integral equations with vector fields of low regularity.
Keywords:stochastic analysis; quasi-sure flows; integral equation