Extremes of multidimensional Gaussian processes

Open Access
Authors
Publication date 2010
Journal Stochastic Processes and their Applications
Volume | Issue number 120 | 12
Pages (from-to) 2289-2301
Organisations
  • Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
Abstract This paper considers extreme values attained by a centered, multidimensional Gaussian process X(t)=(X1(t),…,Xn(t)) minus drift d(t)=(d1(t),…,dn(t)), on an arbitrary set T. Under mild regularity conditions, we establish the asymptotics of \[ \log\pp\left(\exists{t\in T}:\bigcap_{i=1}^n\left\{X_i(t)-d_i(t)>q_iu\right\}\right), \] for positive thresholds qi>0, i=1,…,n and u→∞. Our findings generalize and extend previously known results for the single-dimensional and two-dimensional cases. A number of examples illustrate the theory.
Document type Article
Language English
Published at https://doi.org/10.1016/j.spa.2010.08.010
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