Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random attractors for stochastic evolution equations driven by
  fractional Brownian motion   The main goal of this article is to prove the existence of a random attractor
for a stochastic evolution equation driven by a fractional Brownian motion with
$H\in (1/2,1)$. We would like to emphasize that we do not use the usual
cohomology method, consisting of transforming the stochastic equation into a
random one, but we deal directly with the stochastic equation. In particular,
in order to get adequate a priori estimates of the solution needed for the
existence of an absorbing ball, we will introduce stopping times to control the
size of the noise. In a first part of this article we shall obtain the
existence of a pullback attractor for the non-autonomous dynamical system
generated by the pathwise mild solution of an nonlinear infinite-dimensional
evolution equation with non--trivial H\"older continuous driving function. In a
second part, we shall consider the random setup: stochastic equations having as
driving process a fractional Brownian motion with $H\in (1/2,1)$. Under a
smallness condition for that noise we will show the existence and uniqueness of
a random attractor for the stochastic evolution equation.

37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat