A dynamical theory for singular stochastic delay differential equations I: Linear equations and a Multiplicative Ergodic Theorem on fields of Banach spaces Article Swipe
Related Concepts
Ergodic theory
Mathematics
Banach space
Multiplicative function
C0-semigroup
Eberlein–Šmulian theorem
Pure mathematics
Banach manifold
Mathematical analysis
Lp space
Mazyar Ghani Varzaneh
,
Sebastian Riedel
,
Michael Scheutzow
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1903.01172
· OA: W4288481395
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1903.01172
· OA: W4288481395
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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