A dynamical theory for singular stochastic delay differential equations I: Linear equations and a Multiplicative Ergodic Theorem on fields of Banach spaces
Probability
2019-12-16 v3 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1903.01172,
title = {A dynamical theory for singular stochastic delay differential equations I: Linear equations and a Multiplicative Ergodic Theorem on fields of Banach spaces},
author = {Mazyar Ghani Varzaneh and Sebastian Riedel and Michael Scheutzow},
journal= {arXiv preprint arXiv:1903.01172},
year = {2019}
}