Spectral Representation for Branching Processes with Immigration on the Real Half Line

Abstract

§ Oo Introduction In the previous paper JJT], we have obtained the spectral representation for the semigroups of continuous state branching processes (CBprocesses). In this paper, we shall obtain the analogous results for continuous state branching processes with immigration (CBI-processes). CBI-processes were introduced by Kawazu and Watanabe Q3] as a continuous version of Galton-Watson processes with immigration and our results are similar to those of Karlin and McGregor []2] for GaltonWatson processes with immigration. When CBI-processes are diffusions, our representations are some concrete examples of the general represen