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.
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