The Stable Manifold Theorem for Nonlinear Stochastic Systems with Memory I: Existence of the Semiflow (1999)
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| Venue: | Journal of Functional Analysis |
| Citations: | 14 - 8 self |
BibTeX
@ARTICLE{Mohammed99thestable,
author = {Salah-Eldin A. Mohammed and Michael K. R. Scheutzow},
title = {The Stable Manifold Theorem for Nonlinear Stochastic Systems with Memory I: Existence of the Semiflow},
journal = {Journal of Functional Analysis},
year = {1999},
volume = {205},
pages = {271--305}
}
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Abstract
. We consider non-linear stochastic functional dierential equations (sfde's) on Euclidean space. We give sucient conditions for the sfde to admit locally compact smooth cocycles on the underlying innite-dimensional state space. Our construction is based on the theory of nite-dimensional stochastic ows and a non-linear variational technique. In Part II of this article, the above result will be used to prove a stable manifold theorem for non-linear sfde's. 1.
