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 with continuous paths on the interior,. The domains of attraction of the two different types of self-similar processes are investigated,. Our approach is to establish convergence of excursion point processes, which is based on Ito's excursion theory and a recent result on convergence of excursion measures by Fitzsimmons and the present author.