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

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

2007-05-24

arxiv.org/abs/0705.3588v4

Bernoulli 2008, Vol. 14, No. 4, 963-987

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/08-BEJ132 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ132

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 It\^{o}'s excursion theory and a recent result on convergence of excursion measures by Fitzsimmons and the present author.

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