Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long time behavior of diffusions with Markov switching   Let $Y$ be an Ornstein-Uhlenbeck diffusion governed by an ergodic finite
state Markov process $X$: $dY_t=-\lambda(X_t)Y_tdt+\sigma(X_t)dB_t$, $Y_0$
given. Under ergodicity condition, we get quantitative estimates for the long
time behavior of $Y$. We also establish a trichotomy for the tail of the
stationary distribution of $Y$: it can be heavy (only some moments are finite),
exponential-like (only some exponential moments are finite) or Gaussian-like
(its Laplace transform is bounded below and above by Gaussian ones). The
critical moments are characterized by the parameters of the model.

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The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg