Markov Chain

Markov Chain 

I will keep the notes about Markov Chain in this page. These are just random notes 

Markov Chain Analysis, Author : W. Li, C. Zhang, International Encyclopedia of Human Geography 2009, Pages 455-460

A Markov chain is a process that consists of a finite number of states with the Markovian property and some transition probabilities pij, 
where pij is the probability of the process moving from state i to state j. 
Andrei Markov, a Russian mathematician, was the first one to study this process. At the beginning of last century, 
he developed the fundamentals of the Markov chain theory. Markov chains are traditionally used for one-dimensional time series or spatial series analysis in a variety of fields from economics to stratigraphy. 
Markov chains were extended for multidimensional simulation recently with the proposition of a Markov chain random field theory and its attendant spatial measure – the transiogram. 
This article focuses on introducing basic one-dimensional Markov chain models and recent progress in Markov chain geostatistics – the multidimensional extension of Markov chains.