Random Walk

Published Jan 14, 2023

Definition of Random Walk

A random walk is a mathematical model of a process in which successive steps or movements are determined by chance. That means it describes a path that consists of a sequence of random steps in which the direction and length of each step are determined by a random variable.

Example

To illustrate this, let’s look at a simple example. Imagine a person walking around a city. At each intersection, the person has to decide which direction to go. To make this decision, the person flips a coin. If it lands on heads, the person goes left. If it lands on tails, the person goes right. This process is repeated at every intersection until the person reaches their destination or gets tired of walking around. This is quite a literal example of a random walk.

Why Random Walk Matters

Random walks are used in a variety of fields, such as physics, biology, economics, and finance. In physics, random walks are used to model the behavior of particles in a fluid. In biology, they are used to model the movement of animals. In economics, they are used to model the behavior of stock prices. And in finance, they are used to model the behavior of investors. In all these cases, random walks provide a useful tool for understanding and predicting the behavior of complex systems.