Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bernstein type's concentration inequalities for symmetric Markov
  processes   Using the method of transportation-information inequality introduced in
\cite{GLWY}, we establish Bernstein type's concentration inequalities for
empirical means $\frac 1t \int_0^t g(X_s)ds$ where $g$ is a unbounded
observable of the symmetric Markov process $(X_t)$. Three approaches are
proposed : functional inequalities approach ; Lyapunov function method ; and an
approach through the Lipschitzian norm of the solution to the Poisson equation.
Several applications and examples are studied.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
19
The categories of this paper are: eess