Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremes and first passage times of correlated fBm's   Let $\{X_i(t),t\ge0\}, i=1,2$ be two standard fractional Brownian motions
being jointly Gaussian with constant cross-correlation. In this paper we derive
the exact asymptotics of the joint survival function $$
\mathbb{P}\{\sup_{s\in[0,1]}X_1(s)>u,\ \sup_{t\in[0,1]}X_2(t)>u\} $$ as
$u\rightarrow \infty$. A novel finding of this contribution is the exponential
approximation of the joint conditional first passage times of $X_1, X_2$. As a
by-product we obtain generalizations of the Borell-TIS inequality and the
Piterbarg inequality for 2-dimensional Gaussian random fields.

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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org