Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Properties of Large Excursions of a Stationary Gaussian Process   The present work investigates two properties of level crossings of a
stationary Gaussian process $X(t)$ with autocorrelation function $R_X(\tau)$.
We show firstly that if $R_X(\tau)$ admits finite second and fourth derivatives
at the origin, the length of up-excursions above a large negative level
$-\gamma$ is asymptotically exponential as $-\gamma \to -\infty$. Secondly,
assuming that $R_X(\tau)$ admits a finite second derivative at the origin and
some defined properties, we derive the mean number of crossings as well as the
length of successive excursions above two subsequent large levels. The
asymptotic results are shown to be effective even for moderate values of
crossing level. An application of the developed results is proposed to derive
the probability of successive excursions above adjacent levels during a time
window.

19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol