Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An orthogonal-polynomial approach to first-hitting times of birth-death
  processes   In a recent paper in the Journal of Theoretical Probability Gong, Mao and
Zhang, using the theory of Dirichlet forms, extended Karlin and McGregor's
classical results on first-hitting times of a birth-death process on the
nonnegative integers by establishing a representation for the Laplace transform
$\mathbb{E}[e^{sT_{ij}}]$ of the first-hitting time $T_{ij}$ for $any$ pair of
states $i$ and $j$, as well as asymptotics for $\mathbb{E}[e^{sT_{ij}}]$ when
either $i$ or $j$ tends to infinity. It will be shown here that these results
may also be obtained by employing tools from the orthogonal-polynomial toolbox
used by Karlin and McGregor, in particular $associated$ $polynomials$ and
$Markov's$ $theorem$.

23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an