Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-central limit theorem for non-linear functionals of vector valued
  Gaussian stationary random fields   Here I prove non-central limit theorems for non-linear functionals of vector
valued stationary random fields under appropriate conditions. They are the
multivariate versions of the results in paper\cite{2}. Previously A. M. Arcones
formulated a theorem in paper\cite{1} which can be considered as the
multivariate generalization of these results. But I found Arcones' discussion
incomplete, and in my opinion to give a complete proof first a more profound
foundation of the theory of vector valued Gaussian stationary random fields has
to be worked out. This was done in my paper\cite{4} which enabled me to adapt
the method in paper\cite{2} to the study of the vector valued case. Here I
prove with its help the desired multivariate version of the results in
paper\cite{2}.

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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: cs