Ergodicity in nonautonomous linear ordinary differential equations

M. Pituk, Christian Pötzsche

Research output: Contribution to journalArticle

Abstract

The weak and strong ergodic properties of nonautonomous linear ordinary differential equations are considered. It is shown that if the coefficient matrix function is bounded, essentially nonnegative and uniformly irreducible, then the normalized positive solutions are asymptotically equivalent to the Perron vectors of the strongly positive transition matrix at infinity (weak ergodicity). If, in addition, the coefficient matrix function is uniformly continuous, then the convergence of the normalized positive solutions to the same strongly positive limiting vector (strong ergodicity) is equivalent to the convergence of the Perron vectors of the coefficient matrices.

Original languageEnglish
JournalJournal of Mathematical Analysis and Applications
DOIs
Publication statusPublished - Jan 1 2019

Keywords

  • Ergodicity
  • Hilbert's projective metric
  • Ordinary differential equation
  • Perron–Frobenius theory
  • Positivity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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