Limit laws for the maxima of stationary chi-processes under random index

Zhongquan Tan ^[1] ; Changchun Wu ^[1]
1. [1] Jiaxing University
  
  Jiaxing University
  
  China
Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 23, Nº. 4, 2014, págs. 769-786
Idioma: inglés
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Resumen
- Let {χk(t),t≥0} be a stationary χ-process with k degrees of freedom. In this paper, we consider the maxima Mk(T)=max{χk(t),∀t∈[0,T]} with random index TT, where TT/T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of Mk(TT) exists under some additional conditions.