Ergodicity conditions for upper transition operators

Abstract

We study ergodicity for upper transition operators: bounded, sub-additive and non-negatively homogeneous transformations of finite-dimensional linear spaces. Ergodicity provides a necessary and sufficient condition for Perron-Frobenius-like convergence behaviour for upper transition operators. It can also be characterised alternatively using accessibility relations: ergodicity is equivalent with there being a single maximal communication (or top) class that is moreover regular and absorbing. We present efficient algorithms for checking these conditions. © Springer-Verlag Berlin Heidelberg 2010.