Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Jain-Monrad criterion for rough paths and applications to random
  Fourier series and non-Markovian H\"ormander theory   We discuss stochastic calculus for large classes of Gaussian processes, based
on rough path analysis. Our key condition is a covariance measure structure
combined with a classical criterion due to Jain and Monrad [Ann. Probab. 11
(1983) 46-57]. This condition is verified in many examples, even in absence of
explicit expressions for the covariance or Volterra kernels. Of special
interest are random Fourier series, with covariance given as Fourier series
itself, and we formulate conditions directly in terms of the Fourier
coefficients. We also establish convergence and rates of convergence in rough
path metrics of approximations to such random Fourier series. An application to
SPDE is given. Our criterion also leads to an embedding result for
Cameron-Martin paths and complementary Young regularity (CYR) of the
Cameron-Martin space and Gaussian sample paths. CYR is known to imply Malliavin
regularity and also It\^o-like probabilistic estimates for stochastic integrals
(resp., stochastic differential equations) despite their (rough) pathwise
construction. At last, we give an application in the context of non-Markovian
H\"ormander theory.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess