Frontiers of Mathematics in China >
Maxima and sum for discrete and continuous time Gaussian processes
Received date: 26 Oct 2014
Accepted date: 14 May 2015
Published date: 02 Dec 2015
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We study the asymptotic relation among the maximum of continuous weakly and strongly dependent stationary Gaussian process, the maximum of this process sampled at discrete time points, and the partial sum of this process. It is shown that these two extreme values and the sum are asymptotically independent if the grid of the discrete time points is sufficiently sparse and the Gaussian process is weakly dependent, and asymptotically dependent if the grid points are Pickands grids or dense grids.
Yang CHEN , Zhongquan TAN . Maxima and sum for discrete and continuous time Gaussian processes[J]. Frontiers of Mathematics in China, 2016 , 11(1) : 27 -46 . DOI: 10.1007/s11464-015-0491-x
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