Markov Chain - Formal Definition

Formal Definition

A Markov chain is a sequence of random variables X₁, X₂, X₃, ... with the Markov property, namely that, given the present state, the future and past states are independent. Formally,

The possible values of X_i form a countable set S called the state space of the chain.

Markov chains are often described by a directed graph, where the edges are labeled by the probabilities of going from one state to the other states.