Brazilian Journal of Probability and Statistics

Almost sure central limit theorem for exceedance point processes of stationary sequences

Zhongquan Tan

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Abstract

In this paper, we proved an almost sure central limit theorem for the exceedance point processes of a stationary sequence which satisfy some long range dependence conditions. As a by-product, we obtained the almost sure central limit theorem for the order statistics of the stationary sequence. The obtained results are also extended to the vector of point processes for some strong mixing random sequences.

Article information

Source
Braz. J. Probab. Stat., Volume 29, Number 3 (2015), 717-731.

Dates
Received: July 2013
Accepted: April 2014
First available in Project Euclid: 11 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1433983073

Digital Object Identifier
doi:10.1214/14-BJPS242

Mathematical Reviews number (MathSciNet)
MR3355755

Zentralblatt MATH identifier
1321.60059

Keywords
Almost sure central limit theorem point processes order statistics stationary sequences

Citation

Tan, Zhongquan. Almost sure central limit theorem for exceedance point processes of stationary sequences. Braz. J. Probab. Stat. 29 (2015), no. 3, 717--731. doi:10.1214/14-BJPS242. https://projecteuclid.org/euclid.bjps/1433983073


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