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Durham Research Online
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Random dynamical systems with systematic drift competing with heavy-tailed randomness.

Belitsky, V. and Menshikov, M.V. and Petritis, D. and Vachkovskaia, M. (2016) 'Random dynamical systems with systematic drift competing with heavy-tailed randomness.', Markov processes and related fields., 22 (4). pp. 629-652.

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 Undefined control sequence \BbR with heavy-tailed innovation and then using powerful methods stemming from Lyapunov functions to map the resulting Markov chains into positive semi-martingales.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://math-mprf.org/journal/articles/id1438/
Date accepted:No date available
Date deposited:23 March 2017
Date of first online publication:2016
Date first made open access:23 March 2017

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