Solution
= Solution
Use the equilibrium correspondence from the preceding part. For $i\ne j$,
$$
\widehat\pi_i\widehat P_{ij}=\frac{\pi_iq_{ij}}C.
$$
Consequently the <detailed balance> equations for the <jump chain> hold exactly when those for the <continuous-time Markov chain> hold. The reversibility characterizations already given prove the equivalence. Both chains here are started in their respective <stationary distributions>, which generally differ.