Probability for Statistics and Machine Learning pp 375-400 | Cite as

# Random Walks

## Abstract

We have already encountered the simple random walk a number of times in the previous chapters. Random walks occupy an extremely important place in probability because of their numerous applications, and because of their theoretical connections in suitable limiting paradigms to other important random processes in time. Random walks are used to model the value of stocks in economics, the movement of the molecules of a particle in a liquid medium, animal movements in ecology, diffusion of bacteria, movement of ions across cells, and numerous other processes that manifest random movement in time in response to some external stimuli. Random walks are indirectly of interest in various areas of statistics, such as sequential statistical analysis and testing of hypotheses. They also help a student of probability simply to understand randomness itself better.

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