Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Stochastic Models of Nonlinear Dynamical Systems   We investigate in this work the validity of linear stochastic models for
nonlinear dynamical systems. We exploit as our basic tool a previously proposed
Rayleigh-Ritz approximation for the effective action of nonlinear dynamical
systems started from random initial conditions. The present paper discusses
only the case where the PDF-Ansatz employed in the variational calculation is
``Markovian'', i.e. is determined completely by the present values of the
moment-averages. In this case we show that the Rayleigh-Ritz effective action
of the complete set of moment-functions that are employed in the closure has a
quadratic part which is always formally an Onsager-Machlup action. Thus,
subject to satisfaction of the requisite realizability conditions on the noise
covariance, a linear Langevin model will exist which reproduces exactly the
joint 2-time correlations of the moment-functions. We compare our method with
the closely related formalism of principal oscillation patterns (POP), which,
in the approach of C. Penland, is a method to derive such a linear Langevin
model empirically from time-series data for the moment-functions. The
predictive capability of the POP analysis, compared with the Rayleigh-Ritz
result, is limited to the regime of small fluctuations around the most probable
future pattern. Finally, we shall discuss a thermodynamics of statistical
moments which should hold for all dynamical systems with stable invariant
probability measures and which follows within the Rayleigh-Ritz formalism.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
2
The categories of this paper are: math