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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173980Invariance 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 Itô's excursion theory and a recent result on convergence of excursion measures by Fitzsimmons and the present author.Published in at http://dx.doi.org/10.3150/08-BEJ132 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)ProbabilityConvergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-linetext