Markov Chains
Year: 2008
Type: reference-entry
Abstract: A Markov chain is a collection of random variables with a temporal ordering that have the property that “conditional upon the present, the future does not depend upon the past.” This concept, which can be viewed as a form of something known as the Markov property, is the defining characteristic of the Markov chain. Such systems occur very widely throughout the physical and information sciences as well as in a broad range of other application domains. In addition to their utility in modeling real systems, several computational techniques make use of Markov chains, particularly in the field of Monte Carlo methods. The ubiquity of the Markov chain originates from the fact that such collections lie somewhere between one of independent random variables and a completely general collection, which could be extremely complex to deal with. A sufficient structure is available to allow sophisticated analysis; sufficient generality is available to allow a broad class of systems to be described in terms of Markov chains.
Source: Wiley eBooks
Author: Adam M. Johansen
Institution: University of Bristol
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4240719200