Bernoulli

  • Bernoulli
  • Volume 14, Number 4 (2008), 963-987.

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.

Article information

Source
Bernoulli Volume 14, Number 4 (2008), 963-987.

Dates
First available in Project Euclid: 6 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1225980567

Digital Object Identifier
doi:10.3150/08-BEJ132

Mathematical Reviews number (MathSciNet)
MR2543582

Zentralblatt MATH identifier
1157.60320

Keywords
Feller’s boundary condition functional limit theorems invariance principles Itô’s excursion theory

Citation

Yano, Kouji. Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line. Bernoulli 14 (2008), no. 4, 963--987. doi:10.3150/08-BEJ132. https://projecteuclid.org/euclid.bj/1225980567


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