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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Random Dynamical Systems with Systematic Drift Competing with Heavy-Tailed Randomness

Author(s):
Belitsky, V. ; Menshikov, M. ; Petritis, D. ; Vachkovskaia, M.
Total Authors: 4
Document type: Journal article
Source: Markov Processes and Related Fields; v. 22, n. 4, p. 629-652, 2016.
Web of Science Citations: 0
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. (AU)

FAPESP's process: 09/52379-8 - Stochastic modeling of interacting systems
Grantee:Fabio Prates Machado
Support type: Research Projects - Thematic Grants
FAPESP's process: 11/07000-0 - Random walks and related topics
Grantee:Serguei Popov
Support type: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 11/51509-5 - Externalities and economic behavior
Grantee:Fernando Pigeard de Almeida Prado
Support type: Regular Research Grants