## Bernoulli

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

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

#### 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

#### 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