Asymptotic Properties for Inhomogeneous Iterations of Nonlinear Operators

Abstract

The theorems on weak and strong ergodicity for inhomogeneous products of nonnegative matrices are extended to inhomogeneous iterations of nonlinear positive operators on Euclidean space. In particular some concave version of the Coale–Lopez theorem is presented and applied to a density-dependent Leslie model. The results are obtained, via Hilbert’s projective pseudometric, from general theorems on inhomogeneous iterations of operators mapping a metric space into itself.