Brazilian Journal of Probability and Statistics
- Braz. J. Probab. Stat.
- Volume 29, Number 3 (2015), 717-731.
Almost sure central limit theorem for exceedance point processes of stationary sequences
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.
Braz. J. Probab. Stat., Volume 29, Number 3 (2015), 717-731.
Received: July 2013
Accepted: April 2014
First available in Project Euclid: 11 June 2015
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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