Random dynamical systems with systematic drift competing with heavy-tailed randomness

Belitsky, V.; Menshikov, M.V.; Petritis, D.; Vachkovskaia, M.

Random dynamical systems with systematic drift competing with heavy-tailed randomness

Belitsky, V.; Menshikov, M.V.; Petritis, D.; Vachkovskaia, M.

Authors

V. Belitsky

Professor Mikhail Menshikov mikhail.menshikov@durham.ac.uk
Professor

D. Petritis

M. Vachkovskaia

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.

Citation

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

Journal Article Type	Article
Publication Date	Jan 1, 2016
Deposit Date	Mar 22, 2017
Publicly Available Date	Mar 23, 2017
Journal	Markov processes and related fields.
Print ISSN	1024-2953
Publisher	Polymat
Peer Reviewed	Peer Reviewed
Volume	22
Issue	4
Pages	629-652
Publisher URL	http://math-mprf.org/journal/articles/id1438/