Compound Poisson limit theorems for high-level exceedances of some non-stationary processes
Bellanger, Lise ; Perera, Gonzalo
Bernoulli, Tome 9 (2003) no. 3, p. 497-515 / Harvested from Project Euclid
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.
Publié le : 2003-06-14
Classification:  asymptotically ponderable collections of sets,  compound Poisson process,  convergence,  exceedances,  level sets,  mean occupation measures,  point processes
@article{1065444815,
     author = {Bellanger, Lise and Perera, Gonzalo},
     title = {Compound Poisson limit theorems for high-level exceedances of some non-stationary processes},
     journal = {Bernoulli},
     volume = {9},
     number = {3},
     year = {2003},
     pages = { 497-515},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1065444815}
}
Bellanger, Lise; Perera, Gonzalo. Compound Poisson limit theorems for high-level exceedances of some non-stationary processes. Bernoulli, Tome 9 (2003) no. 3, pp.  497-515. http://gdmltest.u-ga.fr/item/1065444815/