Extremes of multidimensional Gaussian processes

K.G. Debicki, K.M. Kosinski, M.R.H. Mandjes, T. Rolski

Research output: Book/ReportReportAcademic

21 Citations (Scopus)

Abstract

This paper considers extreme values attained by a centered, multidimensional Gaussian process X(t) = (X_1(t), ..., X_n(t)) minus drift d(t) = (d_1(t), ..., d_n(t)), on an arbitrary set T. Under mild regularity conditions, we establish the asymptotics of \[ \log P \left(\exists{t\in T}:\bigcap_{i=1}^n\left\{X_i(t)-d_i(t)>q_iu\right\}\right), \] , for positive thresholds q_i > 0, i = 1, ..., n, and $u \rightarrow \infty$ . Our findings generalize and extend previously known results for the single-dimensional and two-dimensional case. A number of examples illustrate the theory.
Original languageEnglish
Place of PublicationAmsterdam
PublisherCentrum voor Wiskunde en Informatica
Number of pages13
Publication statusPublished - 2010

Publication series

NameCWI Report
VolumePNA-1005

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