Title :
Almost sure central limit theorem on maxima and minima
Author :
Liu Ke ; Ren Xiang ; Jiang Huanjun
Author_Institution :
Sch. of Math. & Syst. Sci., Taishan Univ., Taian, China
Abstract :
We prove an almost sure central limit theorem on maxima and minimal: lim(n → ∞) 1/ log n Σnk=1 1/k(l) (vK <; m K ≤ M K ≤ μK) = e(T+η) a.s. as the Stationary Gaussian sequence with covariance rn under the condition 1/n Σ(k=1) |rk| log l exp {γ|rk|log k } ≪ (log log n)-(1+ε).
Keywords :
Gaussian processes; optimisation; almost sure central limit theorem; maxima; minima; stationary Gaussian sequence; Convergence; Covariance matrix; Educational institutions; Lead; Manganese; Random variables; Almost sure central limit theorem; Stationary Gaussian sequence;
Conference_Titel :
Mechatronic Science, Electric Engineering and Computer (MEC), 2011 International Conference on
Conference_Location :
Jilin
Print_ISBN :
978-1-61284-719-1
DOI :
10.1109/MEC.2011.6025877
