Examples of Markov Chains - A Center-biased Random Walk

A Center-biased Random Walk

Consider a random walk on the number line where, at each step, the position (call it x) may change by +1 (to the right) or -1 (to the left) with probabilities:

(where c is a constant greater than 0)


For example if the constant, c, equals 1, the probabilities of a move to the left at positions x = -2,-1,0,1,2 are given by respectively. The random walk has a centering effect that weakens as c increases.

Since the probabilities depend only on the current position (value of x) and not on any prior positions, this biased random walk satisfies the definition of a Markov chain.

Read more about this topic:  Examples Of Markov Chains

Famous quotes containing the words random and/or walk:

    ... the random talk of people who have no chance of immortality and thus can speak their minds out has a setting, often, of lights, streets, houses, human beings, beautiful or grotesque, which will weave itself into the moment for ever.
    Virginia Woolf (1882–1941)

    Yet if a woman never lets herself go, how will she ever know how far she might have got? If she never takes off her high- heeled shoes, how will she ever know how far she could walk or how fast she could run?
    Germaine Greer (b. 1939)