Extremes of multidimensional Gaussian processes
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| Publication date | 2010 |
| Journal | Stochastic Processes and their Applications |
| Volume | Issue number | 120 | 12 |
| Pages (from-to) | 2289-2301 |
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| 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 |
| Downloads |
Kosinski_Mandjes_enz_StochProc_Appl_2010.pdf
(Final published version)
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