Abstract
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.
Citation
Kouji Yano. "Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line." Bernoulli 14 (4) 963 - 987, November 2008. https://doi.org/10.3150/08-BEJ132
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