Extremes of Lp-norm of vector-valued Gaussian processes with trend

Long Bai*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

1 Citation (Scopus)


Let (Formula presented.) be a Gaussian vector process and (Formula presented.) be a continuous function. The asymptotics of distribution of (Formula presented.), the (Formula presented.) norm for Gaussian finite-dimensional vector, have been investigated in numerous literatures. In this contribution, we are concerned with the exact tail asymptotics of (Formula presented.) with trend (Formula presented.) over (Formula presented.). Both scenarios that (Formula presented.) is locally stationary and non-stationary are considered. Important examples include (Formula presented.) and chi-square processes with trend, i.e. (Formula presented.). These results are of interest in applications in engineering, insurance, and statistics, etc.

Original languageEnglish
Pages (from-to)1111-1144
Number of pages34
Issue number8
Publication statusPublished - 17 Nov 2018
Externally publishedYes


  • -norm
  • Pickands constant
  • Piterbarg constant
  • Tail asymptotics
  • fractional Brownian motion
  • vector-valued Gaussian process

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