A General Result for Markov Processes 1.
Consider the following recipe for a single-step trial
- Generate the trial i ? j via route (a), with probability tij(a)
- Choose a reverse trial j ? i via one of the routes, say (b)
Choose it with probability that it would occur as the j ? i route
Probability = tji(b)/tji
- Accept the (forward) trial as if (a) and (b) were the only routes
This recipe satisfies detailed balance for the overall transition i ? j