Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic response and rare events in Mathieu's equation under
  correlated parametric excitation   We derive an analytical approximation to the probability distribution
function (pdf) for the response of Mathieu's equation under parametric
excitation by a random process with a spectrum peaked at the main resonant
frequency, motivated by the problem of large amplitude ship roll resonance in
random seas. The inclusion of random stochastic excitation renders the
otherwise straightforward response to a system undergoing intermittent
resonances: randomly occurring large amplitude bursts. Intermittent resonance
occurs precisely when the random parametric excitation pushes the system into
the instability region, causing an extreme magnitude response. As a result, the
statistics are characterized by heavy-tails. We apply a recently developed
mathematical technique, the probabilistic decomposition-synthesis method, to
derive an analytical approximation to the non-Gaussian pdf of the response. We
illustrate the validity of this analytic approximation through comparisons with
Monte-Carlo simulations that demonstrate our result accurately captures the
strong non-Gaussianity of the response.

14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas