Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Wellposedness of Path-dependent Multidimensional Forward-backward
  SDE   We study in this paper the wellposedness of path-dependent multidimensional
forward-backward stochastic differential equations (FBSDE). By path-dependent
we mean that the coefficients of the forward-backward SDE at time t can depend
on the whole path of the forward process up to time t. These kinds of
forward-backward SDE appear when solving path-dependent stochastic control
problem by means of variational calculus. At the heart of our analysis is the
construction of a decoupling random field on the path space. We first prove the
existence and the uniqueness of decoupling field on small time interval. Then
by introducing the characteristic BSDE, we show that a global decoupling field
can be constructed by patching local solutions together as long as the solution
of the characteristic BSDE remains bounded. Finally, we show that the solution
of a path-dependent forward-backward SDE is stable.

22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio