Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition of Schramm-Loewner evolution along its curve   We show that, for $\kappa\in(0,8)$, the integral of the laws of two-sided
radial SLE$_\kappa$ curves through different interior points against a measure
with SLE$_\kappa$ Green function density is the law of a chordal SLE$_\kappa$
curve, biased by the path's natural length. We also show that, for $\kappa>0$,
the integral of the laws of extended SLE$_\kappa(-8)$ curves through different
interior points against a measure with a closed formula density restricted in a
bounded set is the law of a chordal SLE$_\kappa$ curve, biased by the path's
capacity length restricted in that set. Another result is that, for
$\kappa\in(4,8)$, if one integrates the laws of two-sided chordal SLE$_\kappa$
curves through different force points on $\mathbb R$ against a measure with
density on $\mathbb R$, then one also gets a law that is absolutely continuous
w.r.t. that of a chordal SLE$_\kappa$ curve. To obtain these results, we
develop a framework to study stochastic processes with random lifetime, and
improve the traditional Girsanov's Theorem.

9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an