Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representation of intermediate time-scale motions in stochastic
  modeling: Analysis on stochastic description of classical Hamiltonian
  dynamics in relation with measurement imperfection   It is a well established result that, in classical dynamical systems with
sufficient time-scale separation, the fast chaotic degrees of freedom are well
modeled by (Gaussian) white noise. In this paper, we present the stochastic
dynamical description for intermediate time-scale motions with insufficient
time-scale separation from the slow dynamical system. First, we analyze how the
fast deterministic dynamics can be viewed as stochastic dynamics under
experimental observation by intrinsic errors of measurement. Then, we present
how the stochastic dynamical description should be modified if intermediate
time-scale motions exist: the time correlation of the noise \xi is modified to
<\xi(t)\xi(t')> = C(x,p)\delta(t-t'), where C(x,p) is a smooth function of the
slow coordinate (x,p), and generally the cumulants of \xi except its average
vary as a smooth function of the slow coordinates (x,p). The analysis given in
this work actually shows that, regardless of the sufficiency of time-scale
separation, any complex (chaotic and ergodic) dynamical system can be well
described using Markov process, if we perfectly construct the deterministic
part of (extended) stochastic dynamics.

10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph