k = 1 £ 1 £ 2 £ k where the infinite series on the RHS is assumed to be convergent.

The equilibrium equation (8.43) can also be obtained from the state transition rate diagram (with respect to k).

Flow rate into the state k = Xk-1 P(k - 1) + £k+1 P(k + 1) and Flow rate out of the state k = (Xk + £k) P(k).

In equilibrium, these two rates must be equal

which is the same as 8.43. The equation (or solution) of equation (8.44) can be obtained by considering the conservation of flow across a vertical plane (Boundary) separating the adjacent states.

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