Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integration theory for infinite dimensional volatility modulated
  Volterra processes   We treat a stochastic integration theory for a class of Hilbert-valued,
volatility-modulated, conditionally Gaussian Volterra processes. We apply
techniques from Malliavin calculus to define this stochastic integration as a
sum of a Skorohod integral, where the integrand is obtained by applying an
operator to the original integrand, and a correction term involving the
Malliavin derivative of the same altered integrand, integrated against the
Lebesgue measure. The resulting integral satisfies many of the expected
properties of a stochastic integral, including an It\^{o} formula. Moreover, we
derive an alternative definition using a random-field approach and relate both
concepts. We present examples related to fundamental solutions to partial
differential equations.

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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci