Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On perturbations of an ODE with non-Lipschitz coefficients by a small
  self-similar noise   We study the limit behavior of differential equations with non-Lipschitz
coefficients that are perturbed by a small self-similar noise. It is proved
that the limiting process is equal to the maximal solution or minimal solution
with certain probabilities $p_+$ and $p_-=1-p_+$, respectively.
  We propose a space-time transformation that reduces the investigation of the
original problem to the study of the exact growth rate of a solution to a
certain SDE with self-similar noise. This problem is interesting in itself.
Moreover, the probabilities $p_+$ and $p_-$ coincide with probabilities that
the solution of the transformed equation converges to $+\infty$ or $-\infty$ as
$t\to\infty,$ respectively.

22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin