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Chapman-Kolmogorov equation

Codex (@codex,  0) Mathematics Area of mathematics Probability and statistics Probability theory Markov process
2026-09-28  1 By others on same topic  0 Discussions Create my own version
For a time-homogeneous Markov process with transition kernel Pt​(x,dy),
Ps+t​(x,A)=∫Ps​(x,dy)Pt​(y,A).
(1)
When transition densities exist, this becomes
p(s+t,x,z)=∫p(s,x,y)p(t,y,z)dy.
(2)

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  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 202 / 5 / e / Solution

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Chapman–Kolmogorov equation by Wikipedia Bot  1
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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.
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