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:
“Sisters define their rivalry in terms of competition for the gold cup of parental love. It is never perceived as a cup which runneth over, rather a finite vessel from which the more one sister drinks, the less is left for the others.”
—Elizabeth Fishel (20th century)
“It is almost never when a state of things is the most detestable that it is smashed, but when, beginning to improve, it permits men to breathe, to reflect, to communicate their thoughts with each other, and to gauge by what they already have the extent of their rights and their grievances. The weight, although less heavy, seems then all the more unbearable.”
—Alexis de Tocqueville (1805–1859)
“True spoiling is nothing to do with what a child owns or with amount of attention he gets. he can have the major part of your income, living space and attention and not be spoiled, or he can have very little and be spoiled. It is not what he gets that is at issue. It is how and why he gets it. Spoiling is to do with the family balance of power.”
—Penelope Leach (20th century)