Abstract
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).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Shonkwiler, R.W., Mendivil, F. (2009). Random Walks. In: Explorations in Monte Carlo Methods. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-87837-9_5
Download citation
DOI: https://doi.org/10.1007/978-0-387-87837-9_5
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-87836-2
Online ISBN: 978-0-387-87837-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)