Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A representation theorem for generators of BSDEs with general growth
  generators in $y$ and its applications   In this paper we first prove a general representation theorem for generators
of backward stochastic differential equations (BSDEs for short) by utilizing a
localization method involved with stopping time tools and approximation
techniques, where the generators only need to satisfy a weak monotonicity
condition and a general growth condition in $y$ and a Lipschitz condition in
$z$. This result basically solves the problem of representation theorems for
generators of BSDEs with general growth generators in $y$. Then, such
representation theorem is adopted to prove a probabilistic formula, in
viscosity sense, of semilinear parabolic PDEs of second order. The
representation theorem approach seems to be a potential tool to the research of
viscosity solutions of PDEs.

7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn