TITLE:
The Moment of Continuous-Time Markov Branching Process with Immigration
AUTHORS:
Juan Wang, Yan Luo
KEYWORDS:
Markov Branching Process, Moment, Immigration, Generating Function
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.4,
April
22,
2025
ABSTRACT: Let
{
Z(
t
),t≥0 }
be a continuous-time Markov branching process with immigration. In this paper, we mainly research the moment for
Z(
t
)
. We calculate the specific expression of the moment
M
1
(
t
)
and then
M
i
(
t
),i>1
can be found subsequently. The moments of the branching process provide great help for further studying the asymptotic behavior of the branching process, so it is indispensable to calculate the moment.