Extremes of vector-valued Gaussian processes with Trend

Long Bai, Krzysztof Dȩbicki, Peng Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Let X(t)=(X1(t),…,Xn(t)),t∈T⊂R be a centered vector-valued Gaussian process with independent components and continuous trajectories, and h(t)=(h1(t),…,hn(t)),t∈T be a vector-valued continuous function. We investigate the asymptotics of P{supt∈T⁡min1≤i≤n⁡(Xi(t)+hi(t))>u} as u→∞. As an illustration to the derived results we analyze two important classes of X(t): with locally-stationary structure and with varying variances of the coordinates, and calculate exact asymptotics of simultaneous ruin probability and ruin time in a Gaussian risk model.

Original languageEnglish
Pages (from-to)47-74
Number of pages28
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 1 Sept 2018
Externally publishedYes


  • Conjunction
  • Extremes
  • Pickands constant
  • Piterbarg constant
  • Vector-valued Gaussian process


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