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arXiv · 1903.01172

A dynamical theory for singular stochastic delay differential equations I: Linear equations and a Multiplicative Ergodic Theorem on fields of Banach spaces

Mazyar Ghani Varzaneh·Sebastian Riedel·Michael Scheutzow
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Abstract

We show that singular stochastic delay differential equations (SDDEs) induce cocycle maps on a field of Banach spaces. A general Multiplicative Ergodic Theorem on fields of Banach spaces is proved and applied to linear SDDEs. In Part II of this article, we use our results to prove a stable manifold theorem for non-linear singular SDDEs.

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Mazyar Ghani Varzaneh, Sebastian Riedel, Michael Scheutzow. 2019-03-04. A dynamical theory for singular stochastic delay differential equations I: Linear equations and a Multiplicative Ergodic Theorem on fields of Banach spaces. https://arxiv.org/abs/1903.01172

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