So far in the second part of this book we have studied Markov transition functions with only informal references to the random variables which actually form the processes themselves. We now turn to this neglected side of our subject. Of necessity, the discussion will have a more measure-theoretical flavor than hitherto. In fact the modern theory of Markov processes has become very complex, because it has been necessary to introduce a great deal of machinery to bridge the gap between intuition about how a process “without memory” should behave, on one hand, and what can be rigorously proved, on the other. Here we will try to keep this machinery as simple as possible, and we will introduce its components only gradually, as they are needed.
KeywordsMarkov Process Transition Function Poisson Process Markov Property Path Function
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