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Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time

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Details

Original languageEnglish
Pages (from-to)433-445
Number of pages13
JournalJOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
Volume30
Issue number2
Early online date22 Aug 2016
DOIs
Publication statusPublished - Jun 2018
Publication typeA1 Journal article-refereed

Abstract

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.

ASJC Scopus subject areas

Keywords

  • $C_0$-semigroups, Asymptotic behaviour, Power-boundeness, Rates of convergence, Recurrence relations, Spectral theory, System

Publication forum classification

Field of science, Statistics Finland