This chapter brings together the discrete-time and continuous-time theories, allowing us to deduce analogues, for continuous-time chains, of all the results given in Chapter 1. All the facts from Chapter 2 that are necessary to understand this synthesis are reviewed in Section 3.1. You will require a reasonable understanding of Chapter 1 here, but, given such an understanding, this chapter should look reassuringly familiar. Exercises remain an important part of the text.
Let I be a countable set. Recall that a Q-matrix on I is a matrix Q = (qij : i,j ∈ I) satisfying the following conditions:
(i) 0 ≤ −qii < ∞ for all i;
(ii) qij ≥ 0 for all i ≠ j;