Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous stochastic processes with non-local memory   We study the non-Markovian random continuous processes described by the
Mori-Zwanzig equation. As a starting point, we use the Markovian Gaussian
Ornstein-Uhlenbeck process and introduce an integral memory term depending on
the past of the process into expression for the higher-order transition
probability function and stochastic differential equation. We show that the
proposed processes can be considered as continuous-time interpolations of
discrete-time higher-order autoregressive sequences. An equation connecting the
memory function (the kernel of integral term) and the two-point correlation
function is obtained. A condition for stationarity of the process is
established. We suggest a method to generate stationary continuous stochastic
processes with prescribed pair correlation function. As illustration, some
examples of numerical simulation of the processes with non-local memory are
presented.

24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph