2012/09/28 by Enkelejd Hashorva, E. Hashorva, Zhichao Weng +1 · 31 citations
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Financial Risk and Volatility Modeling #Gaussian #Gaussian process #Law #Law of large numbers #Limit (mathematics) #Limit of a function #Mathematical analysis #Mathematics #Physics #Random variable #Statistical Methods and Inference #Statistical physics #Statistics #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.1016/j.spl.2012.09.017
published in Statistics & Probability Letters 83(1), 320-330 (Elsevier BV) · A typo in Assumption A2 has been removed
openalex publication_date 2012/09/28 · arxiv created 2014/05/23 · arxiv updated 2014/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we show that the componentwise maxima ofweakly dependent bivariate stationary Gaussian triangular arrays converge in distribution after normalisation to Hüsler-Reiss distribution. Under a strong dependence assumption, we prove that the limit distribution of the maxima is a mixture of a bivariate Gaussian distribution and Hüsler-Reiss distribution. Another finding of our paper is that the componentwise maxima and componentwise minima remain asymptotically independent even in the settings of Hüsler and Reiss (1989) allowing further for weak dependence. Further we derive an almost sure limit theorem under the Berman condition for the components of the triangular array.