Time reversal of a continuous-time Markov chain
= Time reversal of a continuous-time Markov chain
{title2=$q^*_{ij}=\pi_jq_{ji}/\pi_i$}
For an equilibrium chain with strictly positive stationary probabilities, reversed jump rates are $q^*_{ij}=\pi_jq_{ji}/\pi_i$. Under <detailed balance> they equal the original rates, making the stationary path law reversible. Holding times and jump directions reverse together; this is more than symmetry of one-time distributions.