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

Zhongquan Tan () and Changchun Wu

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2014, vol. 23, issue 4, 769-786

Abstract: Let $$\{\chi _{k}(t), t\ge 0\}$$ { χ k ( t ) , t ≥ 0 } be a stationary $$\chi $$ χ -process with $$k$$ k degrees of freedom. In this paper, we consider the maxima $$M_{k}(T)= \max \{\chi _{k}(t), \forall t\in [0,T]\}$$ M k ( T ) = max { χ k ( t ) , ∀ t ∈ [ 0 , T ] } with random index $$\mathcal {T}_{T}$$ T T , where $$\mathcal {T}_{T}/T$$ T T / T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of $$M_{k}(\mathcal {T}_{T})$$ M k ( T T ) exists under some additional conditions. Copyright Sociedad de Estadística e Investigación Operativa 2014

Keywords: Limit theorem; Weak convergence; Maximum; Random index; Stationary Gaussian process; $$\chi $$ χ -process; 60G70; 60F05 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11749-014-0366-6

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