On invariant measures for simple branching processes (Summary)

Abstract

Problems pertaining to invariant measures of a non-critical Galton-Watson process, whether with or without Immigration, may be discussed in terms of measures of a subcritical process with a possibly defective immigration distribution. There is in fact only one such measure satisfying a regular variation condition. This result provides a unifying principle for several contexts of Galton-Watson theory. A full discussion with analytical details will appear elsewhere.