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Type: | Artigo |
Title: | Random Dynamical Systems With Systematic Drift Competing With Heavy-tailed Randomness Random dynamical systems with systematic drift competing with heavy-tailed randomness |
Author: | Belitsky, V. Menshikov, M. V. Petritis, D. Vachkovskaia, M. |
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 ellipticity 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. 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 ellipticity 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. |
Subject: | Markov Chains Recurrence Heavy Tails Moments Of Passage Times Random Dynamical Systems Markov, Processos de Relações de recorrência Sistemas dinâmicos aleatórios |
Country: | Rússia |
Editor: | Polymat |
Citation: | Markov Processes And Related Fields. Polymat, v. 22, p. 629 - 652, 2016. |
Rights: | fechado |
Identifier DOI: | 0 |
Address: | http://math-mprf.org/journal/articles/id1438/ |
Date Issue: | 2016 |
Appears in Collections: | IMECC - Artigos e Outros Documentos |
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