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).
KeywordsBrownian Motion Random Walk Option Price Call Option Electrical Network
Unable to display preview. Download preview PDF.