A dynamical theory for singular stochastic delay differential equations I: Linear equations and a Multiplicative Ergodic Theorem on fields of Banach spaces
13 Dec 2019
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Varzaneh Mazyar Ghani
•
Riedel Sebastian
•
Scheutzow Michael
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.(read more)