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:
“Novels as dull as dishwater, with the grease of random sentiments floating on top.”
—Italo Calvino (1923–1985)
“After climbing a great hill, one only finds that there are many more hills to climb. I have taken a moment here to rest, to steal a view of the glorious vista that surrounds me, to look back on the distance I have come. But I can rest only for a moment, for with freedom comes responsibilities, and I dare not linger, for my long walk is not yet ended.”
—Nelson Mandela (b. 1918)