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Main Title: On the random dynamics of Volterra quadratic operators
Author(s): Jamilov, U. U.
Scheutzow, Michael
Wilke-Berenguer, M.
Type: Article
Language Code: en
Abstract: We consider random dynamical systems generated by a special class of Volterra quadratic stochastic operators on the simplex Sm-1. We prove that in contrast to the deterministic set-up the trajectories of the random dynamical system almost surely converge to one of the vertices of the simplex Sm-1, implying the survival of only one species. We also show that the minimal random point attractor of the system equals the set of all vertices. The convergence proof relies on a martingale-type limit theorem, which we prove in the appendix.
Issue Date: 2015
Date Available: 27-Oct-2017
DDC Class: 510 Mathematik
Sponsor/Funder: DFG, GSC 14, Berlin Mathematical School
Journal Title: Ergodic theory and dynamical systems
Publisher: Cambridge University Press
Publisher Place: Cambridge
Volume: 37
Issue: 1
Publisher DOI: 10.1017/etds.2015.30
Page Start: 228
Page End: 243
EISSN: 1469-4417
ISSN: 0143-3857
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:FG Stochastische Analysis » Publications

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