The application of stochastic processes in function theory

Abstract

(v) A new method which promises to be very useful in the critical case is based on a comparison of generating functions. Consider two age-dependent processes with the same lifelength distribution G, but different particle production generating functions f(s) and h(s). Let F(s, t) and H(s, t) be the corresponding generating functions of the process. Then we have the following age-dependent analog of Spitzer's comparison lemma for the G-W process.