Provide an Excel worksheet for Example 1.2-4 and play a bit, changing the transition matrix and watching what happens. Consider several realizations, generating different random numbers.

Example 1.2-4

Concerns the simulation of Markov chains. A general simulation theory is presented in Section 7.4, but we are able to consider a particular example right away.

The main point is to arrange a random mechanism that allows us to choose states in accordance with transition probabilities. To this end, whatever software we use, we need a generator of random numbers; namely, a program or device that selects at random numbers from the interval [0,1]. For such a generator, the probability that the number will be selected from a subinterval Δ⊆[0,1] is equal to the length of Δ. (See Section 1.2.3.) In Excel, to generate a random number Z, we go to Data⇒Data Analysis ⇒Random Number Generation, and choose in Distributions the position “Uniform” with parameters 0 and 1.