Abstract and Applied Analysis

Abstract and Applied Analysis / 2002 / Article

Open Access

Volume 7 |Article ID 109623 | 9 pages | https://doi.org/10.1155/S1085337502206053

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

Received14 Jun 2002

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.

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.

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