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

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 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/