Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

For questions on random walks, a mathematical formalization of a path that consists of a succession of random steps.

A random walk is a mathematical formalization of a path that consists of a succession of random steps. For example, the price of a fluctuating stock and the financial status of a gambler can all be modeled as random walks, although they may not be truly random in reality. The term random walk was first introduced by Karl Pearson in 1905.

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.

history | excerpt history