Random Walks

Part of the Undergraduate Texts in Mathematics book series (UTM)


While a Markov chain can be considered a random walk (on an appropriate state space), a random walk is not always an instance of a Markov chain. For example, a random walk’s next step could depend on the entire history of the walk up to that time. This is the case for self-avoiding walks, which have applications in the study of macromolecules.

Random walks arise in the motion of particles under collision (such as Brownian motion), in gambling problems (the fortune of a (perhaps unfortunate) gambler), and in mathematical models in finance (such as the pricing of options).


Brownian Motion Random Walk Option Price Call Option Electrical Network 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Mathematics and StatisticsAcadia UniversityWolfvilleCanada

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