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

Gliklikh, Yu. E.; Morozova, L. A.

doi:https://doi.org/10.1155/S1085337502206053

Abstract and Applied Analysis

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

Yu. E. Gliklikh, L. A. Morozova, "On the notion of L 1-completeness of a stochastic flow on a manifold", Abstract and Applied Analysis, vol. 7, Article ID 109623, 9 pages, 2002. https://doi.org/10.1155/S1085337502206053

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

Yu. E. Gliklikh¹ and L. A. Morozova¹

¹Mathematics Faculty, Voronezh State University, Voronezh 394006, Russia

Received14 Jun 2002

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.

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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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