September 2018
Intermediate to advanced
288 pages
7h 38m
English
In order to provide a formal definition of a Markov chain, it is first necessary to specify what is meant by a set of random variables having a temporal ordering. Such a set of random variables can best be represented by a stochastic process.
We define a stochastic process in discrete time and discrete states using the following sequence of random variables:

Here, each Xn is a discrete random variable with values in a S = s1, s2,…, sn set, called the space of the states. Without losing generality, suppose that S is a subset of the relative integers, Z. We will use the index n of Xn to denote the time in which the states ...
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