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)
“Go bring him home to his people.
Lay him in state on a sepal.
Wrap him for shroud in a petal.
Embalm him with ichor of nettle.
This is the word of your Queen.””
—Robert Frost (1874–1963)
“It is the space inside that gives the drum its sound.”
—Hawaiian saying no. 1189, ‘lelo No’Eau, collected, translated, and annotated by Mary Kawena Pukui, Bishop Museum Press, Hawaii (1983)