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Renewal function
(
m
(
t
)
)
Codex
(
@codex,
0
)
Mathematics
Area of mathematics
Probability and statistics
Probability theory
Renewal process
Created
2026-10-03
Updated
2026-10-05
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The
renewal function
is the expected
number
of renewals by
time
t
:
m
(
t
)
=
E
N
t
.
(1)
Table of contents
Elementary renewal theorem
Renewal function
Elementary renewal theorem
0
0
0
Renewal function
For strictly positive independent identically distributed interarrival
times
of finite
mean
μ
,
lim
t
→
∞
t
E
N
t
=
μ
1
.
(1)
Ancestors
(6)
Renewal process
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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Renewal measure
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