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Ergodicity in nonautonomous linear ordinary differential equations
- Source :
- Journal of Mathematical Analysis and Applications. 479:1441-1455
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
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.
- Subjects :
- Mathematics::Dynamical Systems
Applied Mathematics
010102 general mathematics
Ergodicity
Mathematical analysis
Stochastic matrix
Function (mathematics)
01 natural sciences
010101 applied mathematics
Uniform continuity
Bounded function
Convergence (routing)
Ergodic theory
0101 mathematics
Coefficient matrix
Analysis
Mathematics
Subjects
Details
- ISSN :
- 0022247X
- Volume :
- 479
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Analysis and Applications
- Accession number :
- edsair.doi...........5c08f5cd909c39d45b59e0107e865df0