Random Walks

  • Ronald W. Shonkwiler
  • Franklin Mendivil
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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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