Chapman-Kolmogorov equation
= Chapman-Kolmogorov equation
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For a time-homogeneous Markov process with transition kernel $P_t(x,dy)$,
$$
P_{s+t}(x,A)=\int P_s(x,dy)P_t(y,A).
$$
When transition densities exist, this becomes
$$
p(s+t,x,z)=\int p(s,x,y)p(t,y,z)dy.
$$