Markov Chain - Finite State Space

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:

    All finite things reveal infinitude:
    Theodore Roethke (1908–1963)

    Decency ... must be an even more exhausting state to maintain than its opposite. Those who succeed seem to need a stupefying amount of sleep.
    Quentin Crisp (b. 1908)

    But alas! I never could keep a promise. I do not blame myself for this weakness, because the fault must lie in my physical organization. It is likely that such a very liberal amount of space was given to the organ which enables me to make promises, that the organ which should enable me to keep them was crowded out. But I grieve not. I like no half-way things. I had rather have one faculty nobly developed than two faculties of mere ordinary capacity.
    Mark Twain [Samuel Langhorne Clemens] (1835–1910)