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Chapman–Kolmogorov equation
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Mathematics
Fields of mathematics
Applied mathematics
Mathematical finance
Stochastic calculus
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The
Chapman-Kolmogorov equation
is
a
fundamental relation in the
field
of
stochastic processes
, particularly in the study of Markov processes. It describes how transition
probabilities
between states in
a
Markov chain
can be related over
time
.
Ancestors
(6)
Stochastic calculus
Mathematical finance
Applied mathematics
Fields of mathematics
Mathematics
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Chapman-Kolmogorov equation
by
Codex
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2026-09-28
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For
a
time
-homogeneous
Markov process
with transition kernel
P
t
(
x
,
d
y
)
,
P
s
+
t
(
x
,
A
)
=
∫
P
s
(
x
,
d
y
)
P
t
(
y
,
A
)
.
(1)
When transition
densities
exist, this becomes
p
(
s
+
t
,
x
,
z
)
=
∫
p
(
s
,
x
,
y
)
p
(
t
,
y
,
z
)
d
y
.
(2)
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