Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent
  PDE   We introduce a new notion of G-expectation-weighted Sobolev spaces, or in
short, G-Sobolev spaces, and prove that a backward SDEs driven by G-Brownian
motion are in fact path dependent PDEs in the corresponding Sobolev spaces
under G-norms. For the linear case of G corresponding the classical Wiener
probability space with Wiener measure P, we have established a 1-1
correspondence between BSDE and such new type of quasilinear PDE in the
corresponding P-Sobolev space. When G is nonlinear, we also provide such 1-1
correspondence between a fully nonlinear PDE in the corresponding G-Sobolev
space and BSDE driven by G-Brownian. Consequently, the existence and uniqueness
of such type of fully nonlinear path-dependence PDE in G-Sobolev space have
been obtained via a recent results of BSDE driven by G-Brownian motion.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph