The stable manifold theorem for non-linear stochastic systems with memory. I. Existence of the semiflow
نویسندگان
چکیده
منابع مشابه
The stable manifold theorem for non-linear stochastic systems with memory. I. Existence of the semiflow
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 ...
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We state and prove a Local Stable Manifold Theorem (Theorem 4.1) for non-linear stochastic differential systems with finite memory (viz. stochastic functional differential equations (sfde’s)). We introduce the notion of hyperbolicity for stationary trajectories of sfde’s. We then establish the existence of smooth stable and unstable manifolds in a neighborhood of a hyperbolic stationary traject...
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The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts I, II. In Part I (this pap...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2003
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2002.04.001