Abstract
We show the convergence to a compound Poisson process of the high-level exceedances point process Nn(B)=∑j/n∈B1{Xj>un}, where Xn=φ(ξn,Yn), φ is a (regular) regression function, un grows to infinity with n in some suitable way, ξ and Y are mutually independent, ξ 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.
Citation
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
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