Institut für Mathematische Statistik und Wirtschaftsmathematik, Universität Göttingen, D-3400 Göttingen, West Germany
Abstract:
We prove ratio limit theorems for critical ano supercritical branching Ornstein-Uhlenbeck processes. A finite first moment of the offspring distribution {pn} assures convergence in probability for supercritical processes and conditional convergence in probability for critical processes. If even Σpnnlog+log+n< ∞, then almost sure convergence obtains in the supercritical case.