Journal of the Mathematical Society of Japan

Functional limit theorems for processes pieced together from excursions

Kouji YANO

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Abstract

A notion of convergence of excursion measures is introduced. It is proved that convergence of excursion measures implies convergence in law of the processes pieced together from excursions. This result is applied to obtain homogenization theorems of jumping-in extensions for positive self-similar Markov processes, for Walsh diffusions and for the Brownian motion on the Sierpiński gasket.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1859-1890.

Dates
First available in Project Euclid: 27 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1445951170

Digital Object Identifier
doi:10.2969/jmsj/06741859

Mathematical Reviews number (MathSciNet)
MR3417517

Zentralblatt MATH identifier
1344.60035

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60G18: Self-similar processes

Keywords
functional limit theorems excursion theory self-similar processes

Citation

YANO, Kouji. Functional limit theorems for processes pieced together from excursions. J. Math. Soc. Japan 67 (2015), no. 4, 1859--1890. doi:10.2969/jmsj/06741859. https://projecteuclid.org/euclid.jmsj/1445951170


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