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Abstract and Applied Analysis
Volume 7, Issue 12, Pages 627-635
http://dx.doi.org/10.1155/S1085337502206053

On the notion of L1-completeness of a stochastic flow on a manifold

Mathematics Faculty, Voronezh State University, Voronezh 394006, Russia

Received 14 June 2002

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce the notion of L1-completeness for a stochastic flow on manifold and prove a necessary and sufficient condition for a flow to be L1-complete. L1-completeness means that the flow is complete (i.e., exists on the given time interval) and that it belongs to some sort of L1-functional space, natural for manifolds where no Riemannian metric is specified.