Random Walk

A random walk is a process of random steps, motions, or transitions. It might be in one dimension (movement along a line), in two dimensions (movements in a plane), or in three dimensions or more. There are many different types of random walks, characterized by different specifications with respect to dimensions, the role of time, and whether probabilities remain constant, or are state-dependent. The theory of random walks is widely used in many fields. In economics, for example, it might represent price movements of a stock (a one-dimensional model). In ecology, it might represent the movements of an animal seeking food (a two-dimensional model). In physics, it might represent the motion of a particle in space (a three-dimensional model). Often, analysis of the data will attempt to assess whether the behavior differs sufficiently from a random walk to conclude that an alternative model is appropriate.