An elementary example of a random walk is the random walk on the integer number line, $\mathbb {Z}$, which starts at $0$ and at each step moves $+1$ or $−1$ with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be approximated by random walk models, even though they may not be truly random in reality.