Stochastic Processes in Continuous Time

Summary

In the last chapter, we looked first at two specific models, which were later seen to be examples of discrete time Markov chains. We saw how to derive exact probabilities and limiting values for a process having the Markov property, i.e. knowing the current state, we can ignore the path to that state. Similarly, in continuous time, it is a great mathematical convenience to assume this Markov property. We begin by looking at continuous time Markov chains, with some specific applications. The general theory of such chains requires a much deeper mathematical background than is assumed for this book; the excellent texts by Chung (Markov chains with stationary transition probabilities. Springer, Berlin, 1960) and Norris (Markov chains. Cambridge University Press, Cambridge, 1997) provide fascinating reading matter, and justify the assertions we make without proof.