The Conjugacy of Stochastic and Random Differential Equations and the Existence of Global Attractors

@article{Imkeller2001TheCO,
  title={The Conjugacy of Stochastic and Random Differential Equations and the Existence of Global Attractors},
  author={Peter Imkeller and Bj{\"o}rn Schmalfu{\ss}},
  journal={Journal of Dynamics and Differential Equations},
  year={2001},
  volume={13},
  pages={215-249}
}
We consider stochastic differential equations in d-dimensional Euclidean space driven by an m-dimensional Wiener process, determined by the drift vector field f0 and the diffusion vector fields f1,...,fm, and investigate the existence of global random attractors for the associated flows φ. For this purpose φ is decomposed into a stationary diffeomorphism Φ given by the stochastic differential equation on the space of smooth flows on Rd driven by m independent stationary Ornstein Uhlenbeck… Expand
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