This paper considers extreme values attained by a centered, multidimensional Gaussian process 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 the logarithm of the probability that for some t in T, we have that (for all i = 1, ..., n) X_i(t) - d_i(t) > q_i u, for positive thresholds q_i > 0 and u large. Our findings generalize and extend previously known results for the single-dimensional and two-dimensional case. A number of examples illustrate the theory.
Additional Metadata
Keywords Gaussian process, Logarithmic asymptotics
MSC Gaussian processes (msc 60G15)
THEME Logistics (theme 3), Energy (theme 4)
Publisher CWI
Series CWI. Probability, Networks and Algorithms [PNA]
Citation
Dȩbicki, K.G, Kosinski, K, Mandjes, M.R.H, & Rolski, T. (2010). Extremes of multidimensional Gaussian processes. CWI. Probability, Networks and Algorithms [PNA]. CWI.