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 Xi 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.
Read more about this topic: Markov Chain
Famous quotes containing the words formal and/or definition:
“The spiritual kinship between Lincoln and Whitman was founded upon their Americanism, their essential Westernism. Whitman had grown up without much formal education; Lincoln had scarcely any education. One had become the notable poet of the day; one the orator of the Gettsyburg Address. It was inevitable that Whitman as a poet should turn with a feeling of kinship to Lincoln, and even without any association or contact feel that Lincoln was his.”
—Edgar Lee Masters (1869–1950)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)