Bounding the Maximum of Dependent Random Variables
نویسنده
چکیده
Abstract: Let Mn be the maximum of n zero-mean gaussian variables X1, .., Xn with covariance matrix of minimum eigenvalue λ and maximum eigenvalue Λ. Then, for n ≥ 70, Pr{Mn ≥ λ (2 logn− 2.5− log(2 logn− 2.5)) 1 2 − .68Λ} ≥ 1 2 . Bounds are also given for tail probabilities other than 1 2 . Upper bounds are given for tail probabilities of the maximum of dependent identically distributed variables. As an application, the maximum of purely non-deterministic stationary Gaussian processes is shown to have the same first order asymptotic behaviour as the maximum of independent gaussian processes. MSC 2010 subject classifications: 60E15.
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