Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong diffusion approximation in averaging with dynamical systems fast
  motion   The paper deals with the fast-slow motions setups in the continuous time
$\frac {dX^(t)}{dt}=\frac 1\varepsilon
B(X^\varepsilon(t),\xi(t/\varepsilon^2))+b(X^\varepsilon(t),\,\xi(t/\varepsilon^2)),\,
t\in [0,T]$ and the discrete time
$X^\varepsilon((n+1)\varepsilon^2)=X^\varepsilon(n\varepsilon^2)+\varepsilon
B(X^\varepsilon(n\varepsilon^2),\xi(n)) +\varepsilon^2
b(X^\varepsilon(n\varepsilon^2),\xi(n))$, $n=0,1,...,[T/\varepsilon^2]$ where
$\Sigma$ and $b$ are smooth vector functions and $\xi$ is a stationary vector
stochastic process such that $E\xi(0)=0$ for all $x\in\mathbb{R}^d$. Unlike
\cite{Ki20} the assumptions imposed on the process $\xi$ allow applications to
a wide class of observables $g$ in the dynamical systems setup so that $\xi$
can be taken in the form $\xi(t)=g(F^t\xi(0))$ or $\xi(n)=g(F^n\xi(0))$ where
$F$ is either a flow or a diffeomorphism with some hyperbolicity and $g$ is a
vector function. In this paper we show that both $X^\varepsilon$ and a family
of diffusions $\Xi^\varepsilon$ can be redefined on a common sufficiently rich
probability space so that $E\sup_{0\leq t\leq
T}|X^\varepsilon(t)-\Xi^\varepsilon(t)|^{p}\leq C\varepsilon^\delta,\, p\geq 1$
for some $C,\delta>0$ and all $\varepsilon>0$, where all $\Xi^\varepsilon,\,
\varepsilon>0$ have the same diffusion coefficients but underlying Brownian
motions may change with $\varepsilon$.

36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con