2012/12/01 by Z. Tan, Zhongquan Tan, Enkelejd Hashorva +3 · 1 citation
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Analysis of environmental and stochastic processes #Distribution (mathematics) #Distribution function #Function (biology) #Gaussian #Gaussian process #Gaussian random field #Limit (mathematics) #Maxima #Maxima and minima #Point processes and geometric inequalities #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.1239/jap/1354716660
published as J. Appl. Probab. Volume 49, Number 4 (2012), 901-1203 · 11 pages
openalex publication_date 2012/12/01 · arxiv created 2014/04/23 · arxiv updated 2014/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let X n ( t ), t ∈[0,∞), n ∈ℕ, be standard stationary Gaussian processes. The limit distribution of t ∈[0, T ( n )] | X n ( t )| is established as r n ( t ), the correlation function of X n ( t ), t ∈[0,∞), n ∈ℕ, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).