Random dynamical systems with systematic drift competing with heavy-tailed randomnessReport as inadecuate

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1 Instituto de Matematica e Estatistica 2 Department of Mathematical Sciences 3 IRMAR - Institut de Recherche Mathématique de Rennes 4 IMECC - Instituto de Matemática, Estatística e Computação Científica Brésil

Abstract : Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains — ranging from physics to ecology —, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for these systems in the absence of an ellipt-icity condition. More precisely, we classify these systems according to their type and — in the recurrent case — provide with sharp conditions quantifying the nature of recurrence by establishing which moments of passage times exist and which do not exist. The problem is tackled by mapping the random dynamical systems into Markov chains on R with heavy-tailed innovation and then using powerful methods stemming from Lyapunov functions to map the resulting Markov chains into positive semi-martingales.

Keywords : random dynamical systems moments of passage times heavy tails Markov chains recurrence

Author: Vladimir Belitsky - Mikhail Menshikov - Dimitri Petritis - Marina Vachkovskaia -

Source: https://hal.archives-ouvertes.fr/


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