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June 2003 Compound Poisson limit theorems for high-level exceedances of some non-stationary processes
Lise Bellanger, Gonzalo Perera
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Bernoulli 9(3): 497-515 (June 2003). DOI: 10.3150/bj/1065444815

Abstract

We show the convergence to a compound Poisson process of the high-level exceedances point process $N_n(B)= \sum_{j/n\in B} 1_{\{X_j>u_n\}}$, where $X_n=\varphi(\xi_n,Y_n) $, $ \varphi $ is a (regular) regression function, $u_n$ grows to infinity with $n$ in some suitable way, $\xi$ and $Y$ are mutually independent, $\xi$ is stationary and weakly dependent, and $Y$ is non-stationary, satisfying some ergodic conditions. The basic technique is the study of high-level exceedances of stationary processes over suitable collections of random sets.

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Lise Bellanger. Gonzalo Perera. "Compound Poisson limit theorems for high-level exceedances of some non-stationary processes." Bernoulli 9 (3) 497 - 515, June 2003. https://doi.org/10.3150/bj/1065444815

Information

Published: June 2003
First available in Project Euclid: 6 October 2003

zbMATH: 1049.60043
MathSciNet: MR1997494
Digital Object Identifier: 10.3150/bj/1065444815

Rights: Copyright © 2003 Bernoulli Society for Mathematical Statistics and Probability

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Vol.9 • No. 3 • June 2003
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