**Detailed Balance**

For a continuous time Markov chain (CTMC) with transition rate matrix *Q*, if can be found such that for every pair of states *i* and *j*

holds, then the global balance equations are satisfied and is the stationary distribution of the process. If such a solution can be found the resulting equations are usually much easier than directly solving the global balance equations.

A CTMC is reversible if and only if the detailed balance conditions are satisfied for every pair of states *i* and *j*.

A discrete time Markov chains with transition matrix *P* and equilibrium distribution is said to be in detailed balance if for all pairs *i* and *j*,

When a solution can be found, as in the case of a CTMC, the computation is usually much quicker than directly solving.

Read more about this topic: Balance Equation

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