Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 1 / 26I / v / Solution

Use the equilibrium correspondence from the preceding part. For $i\ne j$,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.