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:
“There is a potential 4-6 percentage point net gain for the President [George Bush] by replacing Dan Quayle on the ticket with someone of neutral stature.”
—Mary Matalin, U.S. Republican political advisor, author, and James Carville b. 1946, U.S. Democratic political advisor, author. All’s Fair: Love, War, and Running for President, p. 205, Random House (1994)
“If the twentieth century is to be better than the nineteenth, it will be because there are among us men who walk in Priestley’s footsteps....To all eternity, the sum of truth and right will have been increased by their means; to all eternity, falsehoods and injustice will be the weaker because they have lived.”
—Thomas Henry Huxley (1825–95)