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:
“And catch the gleaming of a random light,
That tells me that the ship I seek is passing, passing.”
—Paul Laurence Dunbar (1872–1906)
“In health of mind and body, men should see with their own eyes, hear and speak without trumpets, walk on their feet, not on wheels, and work and war with their arms, not with engine-beams, nor rifles warranted to kill twenty men at a shot before you can see them.”
—John Ruskin (1819–1900)