Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Karhunen-Lo\`eve Expansions for Axially Symmetric Gaussian Processes:
  Modeling Strategies and $L^2$ Approximations   Axially symmetric processes on spheres, for which the second-order dependency
structure may substantially vary with shifts in latitude, are a prominent
alternative to model the spatial uncertainty of natural variables located over
large portions of the Earth. In this paper, we focus on Karhunen-Lo\`eve
expansions of axially symmetric Gaussian processes. First, we investigate a
parametric family of Karhunen-Lo\`eve coefficients that allows for versatile
spatial covariance functions. The isotropy as well as the longitudinal
independence can be obtained as limit cases of our proposal. Second, we
introduce a strategy to render any longitudinally reversible process
irreversible, which means that its covariance function could admit certain
types of asymmetries along longitudes. Then, finitely truncated
Karhunen-Lo\`eve expansions are used to approximate axially symmetric
processes. For such approximations, bounds for the $L^2$-error are provided.
Numerical experiments are conducted to illustrate our findings.

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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex