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Linear birth process with immigration
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Probability theory
Markov process
Markov chain
Continuous-time Markov chain
Birth-death process
Pure birth process
2026-09-29
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The
pure birth process
with
rates
λ
n
=
α
n
+
β
, where
α
,
β
>
0
, combines linear
reproduction
with
immigration
. Starting from zero, its
mean
satisfies
m
′
(
t
)
=
α
m
(
t
)
+
β
,
m
(
0
)
=
0
,
(1)
and hence
E
N
(
t
)
=
α
β
(
e
α
t
−
1
)
.
(2)
Ancestors
(10)
Pure birth process
Birth-death process
Continuous-time Markov chain
Markov chain
Markov process
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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Incoming links
(2)
Past exam of the mathematics course of the University of Cambridge
/
2010
/
ii
/
Paper 4
/
26I
/
b
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2020
/
ii
/
Paper 1
/
28K
/
c
/
Solution
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