Translator Disclaimer
December 2015 Records from stationary observations subject to a random trend
Raúl Gouet, F. Javier López, Gerardo Sanz
Author Affiliations +
Adv. in Appl. Probab. 47(4): 1175-1189 (December 2015). DOI: 10.1239/aap/1449859805

Abstract

We prove strong convergence and asymptotic normality for the record and the weak record rate of observations of the form Yn = Xn + Tn, n ≥ 1, where (Xn)nZ is a stationary ergodic sequence of random variables and (Tn)n ≥ 1 is a stochastic trend process with stationary ergodic increments. The strong convergence result follows from the Dubins-Freedman law of large numbers and Birkhoff's ergodic theorem. For the asymptotic normality we rely on the approach of Ballerini and Resnick (1987), coupled with a moment bound for stationary sequences, which is used to deal with the random trend process. Examples of applications are provided. In particular, we obtain strong convergence and asymptotic normality for the number of ladder epochs in a random walk with stationary ergodic increments.

Citation

Download Citation

Raúl Gouet. F. Javier López. Gerardo Sanz. "Records from stationary observations subject to a random trend." Adv. in Appl. Probab. 47 (4) 1175 - 1189, December 2015. https://doi.org/10.1239/aap/1449859805

Information

Published: December 2015
First available in Project Euclid: 11 December 2015

zbMATH: 1333.60051
MathSciNet: MR3433301
Digital Object Identifier: 10.1239/aap/1449859805

Subjects:
Primary: 60G10 , 60G70
Secondary: 60F05 , 60F15

Keywords: asymptotic normality , ergodic theorem , random trend , record , stationary process , strong convergence

Rights: Copyright © 2015 Applied Probability Trust

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 4 • December 2015
Back to Top