Semi‐Markov processes and mobility

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. Notes This paper is a revision and extension of my paper 'Mobility as a Semi‐Markov Process,' presented at the Annual Meeting of the American Association for the Advancement of Science in Boston December, 1969. Section 6 on age effects is entirely new. George Masnick and Phillip Sagi have been kind enough to read parts of the manuscript. I have benefitted from discussions with them and with Robert McGinnis and Neil Henry on the nature and use of these models. I also wish to express my appreciation for the support of the Population Council.