A self-excited migration process

Abstract

Processes whose entities would be independent but whose behaviour is influenced by environmental variables, which they in turn affect, are processes with mediated interactions. The independent open migration process with which is associated a random variable, the excitation, is such a process. This self-excited (conditionally) independent open migration process, with finite excitation, is related to a derived process, its piecewise-deterministic analogue. The correspondence gives insight into the process, as well as an equilibrium independence result. A simple example illustrates the presence of paroxysmal phenomena.