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)
“The menu was stewed liver and rice, fricassee of bones, and shredded dog biscuit. The dinner was greatly appreciated; the guests ate until they could eat no more, and Elisha Dyer’s dachshund so overtaxed its capacities that it fell unconscious by its plate and had to be carried home.”
—For the State of Rhode Island, U.S. public relief program (1935-1943)
“In the tale proper—where there is no space for development of character or for great profusion and variety of incident—mere construction is, of course, far more imperatively demanded than in the novel.”
—Edgar Allan Poe (1809–1849)