Markov chains generated by maximizing components of multidimensional extremal processes

A multidimensional inhomogeneous extremal process is defined and it is demonstrated that it belongs to the class of pure jump Markov processes. Let {Zj(t)} be the jth component of the process. Let {J(t)} be a finite state process defined by J(t)=j if Zj(t)=maxkZk(t). It is proved that {J(t)} is an inhomogeneous Markov chain and the transition probabilities of this chain are obtained. The chain {J(t)} provides a framework for modelling mobility processes that are generated from intertemporal utility-maximizing individuals.