PORTUGALIAE MATHEMATICA Vol. 55, No. 4, pp. 465474 (1998) 

Doubly Stochastic Compound Poisson Processes in Extreme Value TheoryHelena FerreiraUniversidade da Beira Interior,R. Marquês d'Ávila e Bolama, 6200 Covilh\ a  PORTUGAL Abstract: For some linear models, chaindependent sequences and doubly stochastic maxautoregressive processes, which do not satisfy the long range dependence condition $\Delta(u_{n})$ from Hsing {\sl et al.} ([7]), the sequence $\{S_{n}\}_{n\ge1}$, of point processes of exceedances of a real level $u_{n}$ by $X_{1},...,X_{n}$, $n\ge1$, converges in distribution to a compound Poisson process with stochastic intensity. Keywords: Extreme value theory; point processes; mixtures of distributions. Classification (MSC2000): 60F05, 60G55 Full text of the article:
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