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

Kouji Yano

doi:10.3150/08-bej132

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arXiv · 0705.3588

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

Kouji Yano

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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.

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Kouji Yano. 2008-11-14. Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line. https://doi.org/10.3150/08-bej132

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