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:
“The finite is annihilated in the presence of the infinite, and becomes a pure nothing. So our spirit before God, so our justice before divine justice.”
—Blaise Pascal (1623–1662)
“In my dreams is a country where the State is the Church and the Church the people: three in one and one in three. It is a commonwealth in which work is play and play is life: three in one and one in three. It is a temple in which the priest is the worshiper and the worshiper the worshipped: three in one and one in three. It is a godhead in which all life is human and all humanity divine: three in one and one in three.”
—George Bernard Shaw (1856–1950)
“And Space with gaunt grey eyes and her brother Time
Wheeling and whispering come,”
—James Elroy Flecker (1884–1919)