Stochastic Economic Growth: An Operator-Theoretic Approach

For many years the trend in macroeconomics has been towards models which are both explicitly stochastic and explicitly dynamic. With these models, researchers seek to replicate and explain observable properties of the major economic time series. One manifestation of this trend towards stochastic dynamic modeling has been increasing use of the inherently dynamic models developed in the field of economic growth. The latter have proved to be suitable not only for the study of growth and development, but also for that of many other areas within macroeconomics, such as business cycles, fiscal policy and public finance. This thesis is a re-examination of the stochastic dynamics arising from some well-known models of economic growth. The focus is particularly on ergodic properties and the existence of stable equilibria, where equilibrium here is defined in the usual stochastic growth sense (i.e., as the stationary distribution of a Markov process). Brief consideration is also given to asymptotic statistical properties of economic time series, such as law of large numbers and central limit tendencies. On one hand, the thesis has been motivated by the availability of new and unexploited techniques for studying the kinds of Markovian systems generated by these models. The techniques in question are operator-theoretic, with a particular focus on integral Markov semigroups in the function space L1. They are particularly well suited to analysis of Markov chains on unbounded state space. On the other hand, motivation also comes from the demand side: new conditions for evaluating the stability of stochastic dynamic models are valuable