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 Itô’s excursion theory and a recent result on convergence of excursion measures by Fitzsimmons and the present author.
Publié le : 2008-11-15
Classification:
Feller’s boundary condition,
functional limit theorems,
invariance principles,
Itô’s excursion theory
@article{1225980567,
author = {Yano, Kouji},
title = {Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line},
journal = {Bernoulli},
volume = {14},
number = {1},
year = {2008},
pages = { 963-987},
language = {en},
url = {http://dml.mathdoc.fr/item/1225980567}
}
Yano, Kouji. Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line. Bernoulli, Tome 14 (2008) no. 1, pp. 963-987. http://gdmltest.u-ga.fr/item/1225980567/