Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extrema of multi-dimensional Gaussian processes over random intervals   This paper studies the joint tail asymptotics of extrema of the
multi-dimensional Gaussian process over random intervals defined as
  $$ P(u):=\mathbb{P}\left\{\cap_{i=1}^n \left(\sup_{t\in[0,\mathcal{T}_i]} (
X_{i}(t) +c_i t )>a_i u \right)\right\}, \ \ \ u\to\infty, $$ where $X_i(t),
t\ge0$, $i=1,2,\cdots,n,$ are independent centered Gaussian processes with
stationary increments, $\boldsymbol{\mathcal{T}}=(\mathcal{T}_1, \cdots,
\mathcal{T}_n)$ is a regularly varying random vector with positive components,
which is independent of the Gaussian processes, and $c_i\in \mathbb{R}$,
$a_i>0$, $i=1,2,\cdots,n$. Our result shows that the structure of the
asymptotics of $P(u)$ is determined by the signs of the drifts $c_i$'s. We also
discuss a relevant multi-dimensional regenerative model and derive the
corresponding ruin probability.

37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ