Bernoulli

  • Bernoulli
  • Volume 9, Number 3 (2003), 497-515.

Compound Poisson limit theorems for high-level exceedances of some non-stationary processes

Lise Bellanger and Gonzalo Perera

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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.

Article information

Source
Bernoulli, Volume 9, Number 3 (2003), 497-515.

Dates
First available in Project Euclid: 6 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.bj/1065444815

Digital Object Identifier
doi:10.3150/bj/1065444815

Mathematical Reviews number (MathSciNet)
MR1997494

Zentralblatt MATH identifier
1049.60043

Keywords
asymptotically ponderable collections of sets compound Poisson process convergence exceedances level sets mean occupation measures point processes

Citation

Bellanger, Lise; Perera, Gonzalo. Compound Poisson limit theorems for high-level exceedances of some non-stationary processes. Bernoulli 9 (2003), no. 3, 497--515. doi:10.3150/bj/1065444815. https://projecteuclid.org/euclid.bj/1065444815


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