Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Forward Backward SDEs in Weak Formulation   Although having been developed for more than two decades, the theory of
forward backward stochastic differential equations is still far from complete.
In this paper, we take one step back and investigate the formulation of FBSDEs.
Motivated from several considerations, both in theory and in applications, we
propose to study FBSDEs in weak formulation, rather than the strong formulation
in the standard literature. That is, the backward SDE is driven by the forward
component, instead of by the Brownian motion noise. We establish the Feyman-Kac
formula for FBSDEs in weak formulation, both in classical and in viscosity
sense. Our new framework is efficient especially when the diffusion part of the
forward equation involves the $Z$-component of the backward equation.

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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
3
The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci