Abstract and Applied Analysis
Volume 7 (2002), Issue 12, Pages 627-635
doi:10.1155/S1085337502206053
On the notion of L 1-completeness of a stochastic flow on a manifold
Mathematics Faculty, Voronezh State University, Voronezh 394006, Russia
Received 14 June 2002
Copyright © 2002 Yu. E. Gliklikh and L. A. Morozova. 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 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.