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Kelly's lemma : ウィキペディア英語版
Kelly's lemma
In probability theory, Kelly's lemma states that for a stationary continuous time Markov chain, a process defined as the time-reversed process has the same stationary distribution as the forward-time process. The theorem is named after Frank Kelly.
==Statement==

For a continuous time Markov chain with state space ''S'' and transition rate matrix ''Q'' (with elements ''q''''ij'') if we can find a set of numbers ''q''ij'' and ''π''''i'' summing to 1 where〔
::\begin
\sum_ \pi_i q'_ &= \sum_ q_ \quad \forall i\in S\\
\pi_i q_ &= \pi_jq_' \quad \forall i,j \in S
\end
then ''q''ij'' are the rates for the reversed process and ''π''''i'' are the stationary distribution for both processes.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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