Maxima and sum for discrete and continuous time Gaussian processes

doi:10.1007/s11464-015-0491-x

Front. Math. China

2016, Vol. 11

Issue (1) : 27-46 https://doi.org/10.1007/s11464-015-0491-x

RESEARCH ARTICLE

Maxima and sum for discrete and continuous time Gaussian processes

Yang CHEN¹,Zhongquan TAN^2,^*(

)

1. School of Mathematics and Physics, Suzhou University of Science and Technology,Suzhou 215009, China
2. College of Mathematics, Physics and Information Engineering, Jiaxing University,Jiaxing 314001, China

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Abstract

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.

Keywords Continuous time process dependence discrete time process extreme value Gaussian process sum

Corresponding Author(s): Zhongquan TAN

Issue Date: 02 December 2015

Cite this article:

Yang CHEN,Zhongquan TAN. Maxima and sum for discrete and continuous time Gaussian processes[J]. Front. Math. China, 2016, 11(1): 27-46.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0491-x
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I1/27

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