Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and uniqueness of reflecting diffusions in cusps   We consider stochastic differential equations with (oblique) reflection in a
$2$-dimensional domain that has a cusp at the origin, i..e. in a neighborhood
of the origin has the form $\{(x_1,x_2):0<x_1\leq\delta_0,\psi_1(x_1)<x_2<\psi_
2(x_1)\}$, with $\psi_1(0)=\psi_2(0)=0$, $\psi_1'(0)=\psi_2'(0)=0$.
  Given a vector field $\gamma$ of directions of reflection at the boundary
points other than the origin, defining directions of reflection at the origin
$\gamma^i(0):=\lim_{x_1\rightarrow 0^{+}}\gamma (x_1,\psi_i(x_1))$, $ i=1,2,$
and assuming there exists a vector $e^{*}$ such that $\langle
e^{*},\gamma^i(0)\rangle >0$, $i=1,2$, and $e^{*}_1>0$, we prove weak existence
and uniqueness of the solution starting at the origin and strong existence and
uniqueness starting away from the origin.
  Our proof uses a new scaling result and a coupling argument.

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The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc