Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logarithmic asymptotics for multidimensional extremes under non-linear
  scalings   Let $\boldsymbol W=\{\boldsymbol W_n:n\in\mathbb N\}$ be a sequence of random
vectors in $\mathbb R^d$, $d\ge 1$. This paper considers the logarithmic
asymptotics of the extremes of $\boldsymbol W$, that is, for any vector
$\boldsymbol q>\boldsymbol 0$ in $\mathbb R^d$, we find $$\log\mathbb
P\left(\exists{n\in\mathbb N}:\boldsymbol W_n> u \boldsymbol q\right),
\quad\text{as} u\to\infty.$$ We follow the approach of the restricted large
deviation principle introduced in Duffy et al. \textit{Logarithmic asymptotics
for the supremum of a stochastic process} (Ann. Appl. Probab., 13:430--445,
2003). That is, we assume that, for every $\boldsymbol q\ge\boldsymbol 0$, and
some scalings $\{a_n\},\{v_n\}$, $\frac{1}{v_n}\log\mathbb P\left(\boldsymbol
W_n/a_n\ge u \boldsymbol q\right)$ has a, continuous in $\boldsymbol q$, limit
$J_{\boldsymbol W}(\boldsymbol q)$. We allow the scalings $\{a_n\}$ and
$\{v_n\}$ to be regularly varying with a positive index. This approach is
general enough to incorporate sequences $\boldsymbol W$, such that the
probability law of $\boldsymbol W_n/a_n$ satisfies the large deviation
principle with continuous, not necessarily convex, rate functions. The formula
for these asymptotics agrees with the seminal papers on this topic.

12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga