Extremes of multidimensional Gaussian processes
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.
|Keywords||Gaussian process, Logarithmic asymptotics|
|MSC||Gaussian processes (msc 60G15)|
|THEME||Logistics (theme 3), Energy (theme 4)|
|Series||CWI. Probability, Networks and Algorithms [PNA]|
Dȩbicki, K.G, Kosinski, K, Mandjes, M.R.H, & Rolski, T. (2010). Extremes of multidimensional Gaussian processes. CWI. Probability, Networks and Algorithms [PNA]. CWI.