Creating a Markov chain

Let's get started by creating a Markov chain, on which the MDP is developed.

A Markov chain describes a sequence of events that comply with the Markov property. It is defined by a set of possible states, S = {s0, s1, ... , sm}, and a transition matrix, T(s, s'), consisting of the probabilities of state s transitioning to state s'. With the Markov property, the future state of the process, given the present state, is conditionally independent of past states. In other words, the state of the process at t+1 is dependent only on the state at t. Here, we use a process of study and sleep as an example and create a Markov chain based on two states, s0 (study) and s1 (sleep). Let's say we have the following transition matrix:

In the next section, we will compute the transition matrix after k steps, and the probabilities of being in each state given an initial distribution of states, such as [0.7, 0.3], meaning there is a 70% chance that the process starts with study and a 30% chance that it starts with sleep.