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 (16231662)
“Society in every state is a blessing, but Government, even in its best state, is but a necessary evil; in its worst state, an intolerable one.”
—Thomas Paine (17371809)
“The true gardener then brushes over the ground with slow and gentle hand, to liberate a space for breath round some favourite; but he is not thinking about destruction except incidentally. It is only the amateur like myself who becomes obsessed and rejoices with a sadistic pleasure in weeds that are big and bad enough to pull, and at last, almost forgetting the flowers altogether, turns into a Reformer.”
—Freya Stark (18931993)