Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Full classification of dynamics for one-dimensional continuous time
  Markov chains with polynomial transition rates   This paper provides full classification of dynamics for continuous time
Markov chains (CTMCs) on the non-negative integers with polynomial transition
rate functions. Such stochastic processes are abundant in applications, in
particular in biology. More precisely, for CTMCs of bounded jumps, we provide
necessary and sufficient conditions in terms of calculable parameters for
explosivity, recurrence vs transience, certain absorption, positive recurrence
vs null recurrence, and implosivity. Simple sufficient conditions for
exponential ergodicity of stationary distributions and quasi-stationary
distributions as well as existence and non-existence of moments of hitting
times are also obtained. Similar simple sufficient conditions for the
aforementioned dynamics together with their opposite dynamics are established
for CTMCs with unbounded jumps. The results generalize respective criteria for
birth-death processes by Karlin and McGregor in the 1960s. Finally, we apply
our results to stochastic reaction networks, an extended class of branching
processes, a general bursty single-cell stochastic gene expression model, and
population processes, none of which are birth-death processes. The approach is
based on a mixture of Lyapunov-Foster type results, semimartingale approach, as
well as estimates of stationary measures.

27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th