Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large deviation principles for SDEs under locally weak monotonicity
  conditions   This paper establishes a Freidlin-Wentzell large deviation principle for
stochastic differential equations(SDEs) under locally weak monotonicity
conditions and Lyapunov conditions. We illustrate the main result of the paper
by showing that it can be applied to SDEs with non-Lipschitzian coefficients,
which can not be covered in the existing literature. These include the
interesting biological models like stochastic Duffing-van der Pol oscillator
model, stochastic SIR model, etc.

34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th