The stable manifold theorem for non-linear stochastic systems with memory. I. Existence of the semiflow |
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| Authors: | Salah-Eldin A Mohammed Michael KR Scheutzow |
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| Institution: | a Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, IL 62901, USA
b Fakultät II, Institut für Mathematik, MA 7-5, Technical University of Berlin, Strasse des 17 Juni 136, D-10623 Berlin, Germany |
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| Abstract: | We consider non-linear stochastic functional differential equations (sfde's) on Euclidean space. We give sufficient conditions for the sfde to admit locally compact smooth cocycles on the underlying infinite-dimensional state space. Our construction is based on the theory of finite-dimensional stochastic flows 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. |
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| Keywords: | primary 60H10 60H20 secondary 60H25 |
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