Semi‐Markov processes and mobility†

TLDR: In this article, a stochastic model of migration, occupational and vertical mobility, based on the theory of Semi-Markov processes, is presented and important features of these processes derived.

Abstract: A stochastic model of migration, occupational and vertical mobility, based on the theory of Semi‐Markov processes, is presented and important features of these processes derived. The model is a generalization of the Markov process in which the probability of leaving a state can depend in any arbitrary way on the length of time the state has been occupied (duration‐of‐stay) and on the next state entered (pushes and pulls). For mobility processes it thus captures McGinnis’ ‘axiom of cumulative inertia.’ Several distributions with cumulative inertia are presented and the relationship between the Semi‐Markov model and the Mover‐Stayer model explored. A method of including age effects is described. The model is shown to have applications to many other social processes, in addition to mobility, which have duration‐of‐stay effects.