Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusion processes satisfying a conservation law constraint   We investigate coupled stochastic differential equations governing N
non-negative continuous random variables that satisfy a conservation principle.
In various fields a conservation law requires that a set of fluctuating
variables be non-negative and (if appropriately normalized) sum to one. As a
result, any stochastic differential equation model to be realizable must not
produce events outside of the allowed sample space. We develop a set of
constraints on the drift and diffusion terms of such stochastic models to
ensure that both the non-negativity and the unit-sum conservation law
constraint are satisfied as the variables evolve in time. We investigate the
consequences of the developed constraints on the Fokker-Planck equation, the
associated system of stochastic differential equations, and the evolution
equations of the first four moments of the probability density function. We
show that random variables, satisfying a conservation law constraint,
represented by stochastic diffusion processes, must have diffusion terms that
are coupled and nonlinear. The set of constraints developed enables the
development of statistical representations of fluctuating variables satisfying
a conservation law. We exemplify the results with the bivariate beta process
and the multivariate Wright-Fisher, Dirichlet, and Lochner's generalized
Dirichlet processes.

20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con