Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sufficient Conditions for Polynomial Asymptotic Behaviour of the
  Stochastic Pantograph Equation   This paper studies the asymptotic growth and decay properties of solutions of
the stochastic pantograph equation with multiplicative noise. We give
sufficient conditions on the parameters for solutions to grow at a polynomial
rate in $p$-th mean and in the almost sure sense. Under stronger conditions the
solutions decay to zero with a polynomial rate in $p$-th mean and in the almost
sure sense. When polynomial bounds cannot be achieved, we show for a different
set of parameters that exponential growth bounds of solutions in $p$-th mean
and an almost sure sense can be obtained. Analogous results are established for
pantograph equations with several delays, and for general finite dimensional
equations.

30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
3
The categories of this paper are: physics
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio