Sample-Path Stability of Non-Stationary Dynamic Economic Systems
The goal of this paper is to introduce and illustrate a new approach to the stability analysis of sample-paths of nonlinear stochastic economic models with non-stationary components. We place our study within the mathematical theory of random dynamical systems and apply the concept of a random fixed point which is tailor-made for the study of the long-term behavior of sample-paths in stochastic systems. The main tool for the application of this approach is a Banach-type fixed point theorem for non-stationary random dynamical systems which is proved here. The concept and the theorem are thoroughly explained and illustrated by two examples from stochastic growth theory.
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