Disequilibrium Dynamics with Random Perturbations

Abstract

An analysis of the role of random perturbations for the dynamics of business cycles in macroeconomic models still represents one of the most challenging tasks in economic theory. The approach taken in Chapter 4 for equilibrium dynamics introduced some new and useful concepts which allowed a dynamic analysis of stochastic phenomena, i.e. the possibility to provide an investigation of stability and convergence properties of random time series as well as to exhibit their time-invariant statistical properties induced by the stationary orbits. They allow a complete analysis of random data under their transient as well as their stationary or time-invariant behavior within the same mathematical framework. The central issue here will be to apply these methods to the disequilibrium setting in order to characterize and show the main features of the cyclical nature of real and monetary phenomena resulting from the interplay of the time-one map under disequilibrium and random perturbations.