Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analyzing a stochastic process driven by Ornstein-Uhlenbeck noise   A scalar Langevin-type process $X(t)$ that is driven by Ornstein-Uhlenbeck
noise $\eta(t)$ is non-Markovian. However, the joint dynamics of $X$ and $\eta$
is described by a Markov process in two dimensions. But even though there
exists a variety of techniques for the analysis of Markov processes, it is
still a challenge to estimate the process parameters solely based on a given
time series of $X$. Such a partially observed 2D-process could, e.g., be
analyzed in a Bayesian framework using Markov chain Monte Carlo methods.
Alternatively, an embedding strategy can be applied, where first the joint
dynamic of $X$ and its temporal derivative $\dot X$ is analyzed. Subsequently
the results can be used to determine the process parameters of $X$ and $\eta$.
In this paper, we propose a more direct approach that is purely based on the
moments of the increments of $X$, which can be estimated for different
time-increments $\tau$ from a given time series. From a stochastic
Taylor-expansion of $X$, analytic expressions for these moments can be derived,
which can be used to estimate the process parameters by a regression strategy.

30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol