Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large Deviations Principle for a Large Class of One-Dimensional Markov
  Processes   We study the large deviations principle for one dimensional, continuous,
homogeneous, strong Markov processes that do not necessarily behave locally as
a Wiener process. Any strong Markov process $X_{t}$ in $\mathbb{R}$ that is
continuous with probability one, under some minimal regularity conditions, is
governed by a generalized elliptic operator $D_{v}D_{u}$, where $v$ and $u$ are
two strictly increasing functions, $v$ is right continuous and $u$ is
continuous. In this paper, we study large deviations principle for Markov
processes whose infinitesimal generator is $\epsilon D_{v}D_{u}$ where
$0<\epsilon\ll 1$. This result generalizes the classical large deviations
results for a large class of one dimensional "classical" stochastic processes.
Moreover, we consider reaction-diffusion equations governed by a generalized
operator $D_{v}D_{u}$. We apply our results to the problem of wave front
propagation for these type of reaction-diffusion equations.

30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org