Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuity of the Feynman-Kac formula for a generalized parabolic
  equation   It is well-known since the work of Pardoux and Peng [12] that Backward
Stochastic Differential Equations provide probabilistic formulae for the
solution of (systems of) second order elliptic and parabolic equations, thus
providing an extension of the Feynman-Kac formula to semilinear PDEs, see also
Pardoux and Rascanu [14]. This method was applied to the class of PDEs with a
nonlinear Neumann boundary condition first by Pardoux and Zhang [15]. However,
the proof of continuity of the extended Feynman-Kac formula with respect to x
(resp. to (t,x)) is not correct in that paper. Here we consider a more general
situation, where both the equation and the boundary condition involve the
(possibly multivalued) gradient of a convex function. We prove the required
continuity. The result for the class of equations studied in [15] is a
Corollary of our main results.

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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an