Markov Chain - Finite State Space

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:

    All finite things reveal infinitude:
    Theodore Roethke (1908–1963)

    Governments which have a regard to the common interest are constituted in accordance with strict principles of justice, and are therefore true forms; but those which regard only the interest of the rulers are all defective and perverted forms, for they are despotic, whereas a state is a community of freemen.
    Aristotle (384–322 B.C.)

    Play is a major avenue for learning to manage anxiety. It gives the child a safe space where she can experiment at will, suspending the rules and constraints of physical and social reality. In play, the child becomes master rather than subject.... Play allows the child to transcend passivity and to become the active doer of what happens around her.
    Alicia F. Lieberman (20th century)