Stationary equations in continuous time Markov chains

This is a fundamental theorem on stationary distributions of Markov chains, and in applied probability, operations research, etc., the equations (1.3) are frequently solved or manipulated to obtain the limiting, stationary probabilities. The theorem is due to Foster [7] with an earlier, less general version being given by Feller [6, p. 325] (see also Chung [1, p. 33]). In the null recurrent case the existence and uniqueness of a non-negative solution to the equations (1.3) without the condition of absolute convergence