Markov chains generated by maximizing components of multidimensional extremal processes

Abstract

A multidimensional inhomogenous extremal process is defined and it is demonstrated that it belongs to the class of pure jump Markov processes. Let {Z.(t)} be the j-th component of the process. Let {J(t)} be a finite state arocess defined by J(t) j if Z.(t) max Z i,(t). It is proved that {J(t)i is an inhomogenous Markov chaiR and the traRsition probabilities of this chain are obtained. The chain {J(t)} provides a framework for modelling mobility processes that are generated from intertemporal utilitymaximizing individuals.