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Markov Chains by J. R. Norris

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3Continuous-time Markov chains II

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.

3.1 Basic properties

Let I be a countable set. Recall that a Q-matrix on I is a matrix Q = (qij : i,jI) satisfying the following conditions:

      (i)   0 ≤ −qii < ∞    for all    i;

      (ii)   qij ≥ 0    for all    ij;

     (iii)    ...

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