Finite State Space
If the state space is finite, the transition probability distribution can be represented by a matrix, called the transition matrix, with the (i, j)th element of P equal to
Since each row of P sums to one and all elements are non-negative, P is a right stochastic matrix.
Read more about this topic: Markov Chain
Famous quotes containing the words finite, state and/or space:
“God is a being of transcendent and unlimited perfections: his nature therefore is incomprehensible to finite spirits.”
—George Berkeley (1685–1753)
“People think they have taken quite an extraordinarily bold step forward when they have rid themselves of belief in hereditary monarchy and swear by the democratic republic. In reality, however, the state is nothing but a machine for the oppression of one class by another, and indeed in the democratic republic no less than in the monarchy.”
—Friedrich Engels (1820–1895)
“In bourgeois society, the French and the industrial revolution transformed the authorization of political space. The political revolution put an end to the formalized hierarchy of the ancien regimé.... Concurrently, the industrial revolution subverted the social hierarchy upon which the old political space was based. It transformed the experience of society from one of vertical hierarchy to one of horizontal class stratification.”
—Donald M. Lowe, U.S. historian, educator. History of Bourgeois Perception, ch. 4, University of Chicago Press (1982)