Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line

摘要

Invariance principles are obtained for a Markov process on a half-line withcontinuous paths on the interior. The domains of attraction of the twodifferent types of self-similar processes are investigated. Our approach is toestablish convergence of excursion point processes, which is based on It\^{o}'sexcursion theory and a recent result on convergence of excursion measures byFitzsimmons and the present author.