Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Geometry of Filtering   Geometry arising from two diffusion operators (smooth semi-elliptic, second
order differential operators) on different spaces but intertwined by a smooth
map is described. Particular cases arise from Riemannian submersions when the
operators are Laplace-Beltrami operators, from equivariant operators on the
total space of a principal bundle, and for the operators on the diffeomorphism
group arising from stochastic flows. Classical non-linear filtering problems
also lead to such conffigurations. A basic tool is the, possibly, non-linear
"semi-connection" induced by this set up, leading to a canonical decomposition
of the operator on the domain space. Topics discussed include: generalised
Wietzenbock curvatures arising in the equivariant case, skew -product
decompositions of diffusion processes, conditioned processes, classical
filtering, decomposition of stochastic flows, and connections determined by
stochastic differential equations.

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The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom