Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: G{\^a}teaux type path-dependent PDEs and BSDEs with Gaussian forward
  processes   We are interested in path-dependent semilinear PDEs, where the derivatives
are of G{\^a}teaux type in specific directions k and b, being the kernel
functions of a Volterra Gaussian process X. Under some conditions on k, b and
the coefficients of the PDE, we prove existence and uniqueness of a decoupled
mild solution, a notion introduced in a previous paper by the authors. We also
show that the solution of the PDE can be represented through BSDEs where the
forward (underlying) process is X.

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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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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: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an