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

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arxiv 1903.01172 v3 pith:Z66UMIDA submitted 2019-03-04 math.PR math.DS

Mazyar Ghani Varzaneh , Sebastian Riedel , Michael Scheutzow This is my paper · ORCID
classification math.PRmath.DS
keywords banachequationssddessingularspacestheoremdelaydifferential
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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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  1. Dynamics of Stochastic Reaction-Diffusion Equations

    math.PR 2019-08 conditional novelty 2.0 of 10

    This survey maps solution theory and dynamics of stochastic reaction-diffusion equations, reporting known results rather than proving new ones.

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