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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

· 2019 · math.PR · arXiv 1903.01172

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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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  • Dynamics of Stochastic Reaction-Diffusion Equations math.PR · 2019-08-24 · conditional · none · ref 90 · internal anchor

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