Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremes of vector-valued Gaussian processes: exact asymptotics   Let $\{X_i(t),t\ge0\}, 1\le i\le n$ be mutually independent centered Gaussian
processes with almost surely continuous sample paths. We derive the exact
asymptotics of $$ P\left(\exists_{t \in [0,T]}
  \forall_{i=1 ... n} X_i(t)> u \right) $$ as $u\to\infty$, for both locally
stationary $X_i$'s and $X_i$'s with a non-constant generalized variance
function. Additionally, we analyze properties of multidimensional counterparts
of the Pickands and Piterbarg constants, that appear in the derived
asymptotics. Important by-products of this contribution are the vector-process
extensions of the Piterbarg inequality, the Borell-TIS inequality, the Slepian
lemma and the Pickands-Piterbarg lemma which are the main pillars of the
extremal theory of vector-valued Gaussian processes.

4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph