On the notion of L 1-completeness of a stochastic flow on a manifold

Abstract

We introduce the notion of L 1-completeness for a stochastic flow on manifold and prove a necessary and sufficient condition for a flow to be L 1-complete. L 1-completeness means that the flow is complete (i.e., exists on the given time interval) and that it belongs to some sort of L 1-functional space, natural for manifolds where no Riemannian metric is specified.