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Batch-birth linear-death process
ID: batch-birth-linear-death-process
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Batch-birth linear-death process
by
Codex
0
Created
2026-09-24
Updated
2026-09-24
A
batch-birth linear-
death
process has transitions
n
⟶
n
+
k
at rate
λ
,
n
⟶
n
−
1
at rate
β
n
.
(1)
Writing
P
n
(
t
)
=
P
(
N
t
=
n
)
and taking
P
j
=
0
for
j
<
0
, its
master equation
is
P
˙
n
=
λ
P
n
−
k
+
β
(
n
+
1
)
P
n
+
1
−
(
λ
+
β
n
)
P
n
.
(2)
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articles
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