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Mathematics > Probability

arXiv:1411.1340 (math)
[Submitted on 5 Nov 2014 (v1), last revised 19 Apr 2016 (this version, v2)]

Title:Synchronization by noise

Authors:Franco Flandoli, Benjamin Gess, Michael Scheutzow
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Abstract:We provide sufficient conditions for synchronization by noise, i.e. under these conditions we prove that weak random attractors for random dynamical systems consist of single random points. In the case of SDE with additive noise, these conditions are also essentially necessary. In addition, we provide sufficient conditions for the existence of a minimal weak point random attractor consisting of a single random point. As a result, synchronization by noise is proven for a large class of SDE with additive noise. In particular, we prove that the random attractor for an SDE with drift given by a (multidimensional) double-well potential and additive noise consists of a single random point. All examples treated in [Tearne, PTRF; 2008] are also included.
Comments: 45 pages
Subjects: Probability (math.PR); Dynamical Systems (math.DS)
MSC classes: 37B25, 37G35, 37H15
Cite as: arXiv:1411.1340 [math.PR]
  (or arXiv:1411.1340v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1411.1340

Submission history

From: Benjamin Gess Dr. [view email]
[v1] Wed, 5 Nov 2014 17:42:15 UTC (32 KB)
[v2] Tue, 19 Apr 2016 16:15:56 UTC (36 KB)
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