Building the Stochastic Matrix

This chapter describes the method by which a transition matrix of a two-state Markov chain can be obtained from a sequence of events or from some relative observations expressed in percentages. Transition probabilities can be retrieved from known events. Mutually exclusive events can be very useful for modeling a discrete-time Markov chain. The probability of events can be deduced from relative observations. Such observations may consist of values provided in percentages. Moreover, a two-state Markov chain can be represented by a right stochastic matrix made from two probability vectors positioned one over the other. Each probability vector includes two values (components). Taken separately, the two probability vectors can be regarded as representatives for independent variables. The transition probabilities of a two-state Markov chain can be easily determined if the observations are provided in percentages.