Ergodicity beyond asymptotically autonomous linear difference equations

M. Pituk, Christian Pötzsche

Research output: Contribution to journalArticle

Abstract

It is known that if the coefficient matrix of a linear autonomous difference equation is nonnegative and primitive, then the solutions starting from nonnegative nonzero initial data are strongly ergodic. The strong ergodic property of the nonnegative solutions was earlier extended to equations with asymptotically constant coefficients. In this paper, we present a generalization of the previous results by showing that the nonnegative solutions satisfy a similar ergodic property also in some cases when the coefficient matrices are not asymptotically constant.

Original languageEnglish
Pages (from-to)149-156
Number of pages8
JournalApplied Mathematics Letters
Volume86
DOIs
Publication statusPublished - Dec 1 2018

Keywords

  • Difference equation
  • Ergodicity
  • Nonnegative solution
  • Perron–Frobenius theory

ASJC Scopus subject areas

  • Applied Mathematics

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