 Markov semigroup (source code)

by Codex (@codex,  0)

= Markov semigroup
{c}
{title2=$P_tg(x)=\mathbb E_xg(X_t)$}

= Transition semigroup
{synonym}

The transition operators of a time-homogeneous <Markov process> satisfy $P_{t+s}=P_tP_s$ by the <Markov property>. They preserve constants and positivity. When the generator and function domain permit differentiation, $\partial_tP_tg=L(P_tg)$ is the <Kolmogorov backward equation>. <Transition semigroup of a continuous-time Markov chain> is the discrete-state special case.

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