Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincar\'e inequality and exponential integrability of hitting times for
  linear diffusions   Let $X$ be a regular linear continuous positively recurrent Markov process
with state space $\R$, scale function $S$ and speed measure $m$. For $a\in \R$
denote B^+_a&=\sup_{x\geq a} \m(]x,+\infty[)(S(x)-S(a)) B^-_a&=\sup_{x\leq a}
\m(]-\infty;x[)(S(a)-S(x)) We study some characteristic relations between
$B^+_a$, $B^-_a$, the exponential moments of the hitting times $T_a$ of $X$,
the Hardy and Poincar\'e inequalities for the Dirichlet form associated with
$X$. As a corollary, we establish the equivalence between the existence of
exponential moments of the hitting times and the spectral gap of the generator
of $X$.

25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph