On Global Stability of Some Stochastic Economic Processes: A Synthesis

Abstract

This chapter presents a systematic and unified exposition of those continuous-time dynamic processes that can be formally described by diffusion processes. Such processes are Markovian with continuous sample paths, with probability one, and are of interest for a number of reasons. Continuous-time Markov processes have richer structures, and not every discrete-time Markov process can be imbedded in a continuous-time process; it is possible to exploit such structures effectively to derive powerful stability results circumventing the awkward cycling problems that arise in discrete-time versions and are often quite nonintuitive. It is also possible to obtain analytical characteristics of steady states that are relevant in comparative statics and dynamics. There are significant qualitative differences in the nature of steady states and in the global dynamic behavior even in relatively simple aggregative models. The stability property is even stronger than the variables converging weakly (or in distribution) to the invariant distribution.