The Simulate worksheet performs a discrete event simulation of the Markov Chain. Starting from a specified state, the stochastic process is simulated for 20 or more steps using a Monte Carlo simulation. The number of steps in the display is set when the worksheet is created. Additional steps can be simulated by clicking on the More button. Charts can be made of the state, state value, cumulative value or discounted value. While all the other worksheets show probability distributions or expected values over collections of realizations, the simulation shows a single realization of the process. The presentation helps illustrate the dynamic nature of a stochastic process and the statistical affects of observing the process for a finite number of steps.
This worksheet computes statistics based on the simulation. The count rows accumulate the numbers of observations in the several states, while the frequency row shows the proportions of time that the system was observed in the states.