Ergodicity beyond asymptotically autonomous linear difference equations. (December 2018)

• Record Type: Journal Article
• Authors: Pituk, Mihály; Pötzsche, Christian
• Is Part Of: Applied mathematics letters. Volume 86(2018)
• Page Start: 149
• Page End: 156
• Publication Date: 2018-12
• Subjects: Difference equation -- Nonnegative solution -- Perron–Frobenius theory -- Ergodicity; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.06.030
• Languages: English
• ISSNs: 0893-9659

Abstract

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.