Extremes of L^p-norm of Vector-valued Gaussian processes with Trend

2017/06/26 by Bai, Long
#60G15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1706.08360

Abstract

Let \boldsymbolX(t)=(X₁(t),…,X_d(t)) be a Gaussian vector process and g(t) be a continuous function. The asymptotics of distribution of ‖\boldsymbolX(t)‖_p, the L^p norm for Gaussian finite-dimensional vector, have been investigated in numerous literatures. In this contribution we are concerned with the exact tail asymptotics of ‖\boldsymbolX(t)‖^c_p, c>0, with trend g(t) over [0,T]. Both scenarios that \boldsymbolX(t) is locally stationary and non-stationary are considered. Important examples include ∑_i=1^d |X_i(t)|+g(t) and chi-square processes with trend, i.e., ∑_i=1^d X_i²(t)+g(t). These results are of interest in applications in engineering, insurance and statistics, etc.

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