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August 2017 Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Sandro Vaienti
Ann. Inst. H. Poincaré Probab. Statist. 53(3): 1341-1370 (August 2017). DOI: 10.1214/16-AIHP757

Abstract

We develop and generalise the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical systems, in particular to sequential dynamical systems, given by uniformly expanding maps, and to a few classes of random dynamical systems. Some examples are presented and worked out in detail.

Nous développons et généralisons la théorie des valeurs extrêmes pour des processus stochastiques non-stationnaires, en affaiblissant la condition de mélange uniforme qui avait été utilisée auparavant. Nous appliquons nos résultats à des systèmes dynamiques non autonomes, en particulier aux systèmes dynamiques séquentiels engendrés par des applications dilatantes et à une large classe de systèmes dynamiques aléatoires. Quelques exemples sont présentés et calculés en détail.

Citation

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Ana Cristina Moreira Freitas. Jorge Milhazes Freitas. Sandro Vaienti. "Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems." Ann. Inst. H. Poincaré Probab. Statist. 53 (3) 1341 - 1370, August 2017. https://doi.org/10.1214/16-AIHP757

Information

Received: 1 December 2015; Revised: 4 April 2016; Accepted: 6 April 2016; Published: August 2017
First available in Project Euclid: 21 July 2017

zbMATH: 1375.37026
MathSciNet: MR3689970
Digital Object Identifier: 10.1214/16-AIHP757

Subjects:
Primary: 37A25, 37A50, 37B20, 60G70

Rights: Copyright © 2017 Institut Henri Poincaré

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Vol.53 • No. 3 • August 2017
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