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:
“For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
—Ralph Waldo Emerson (1803–1882)
“To the cry of “follow Mormons and prairie dogs and find good land,” Civil War veterans flocked into Nebraska, joining a vast stampede of unemployed workers, tenant farmers, and European immigrants.”
—For the State of Nebraska, U.S. public relief program (1935-1943)
“For good teaching rests neither in accumulating a shelfful of knowledge nor in developing a repertoire of skills. In the end, good teaching lies in a willingness to attend and care for what happens in our students, ourselves, and the space between us. Good teaching is a certain kind of stance, I think. It is a stance of receptivity, of attunement, of listening.”
—Laurent A. Daloz (20th century)