MARKOV AND THE BIRTH OF CHAIN DEPENDENCE THEORY

Markov's work on chain dependence was motivated by his desire to refut e a statement by Nekrasov that pairwise independence of random summand s was a necessary condition for the Weak Law of Large Numbers. He did this by obtaining such a Law in 1906 for systems of dependent random v ariables, in particular for finite homogeneous 'Markov' chains. Nekras ov's incorrect assertion arose out of the theological doctrine of free will, with which some members of the Moscow School of Mathematics of the time were much concerned, The first part of the paper presents the background to the above. The second part deals with the somewhat negl ected techniques of Markov's 1906 paper, especially his use of what is now known as the ergodicity coefficient, to express the contractive e ffect of applying a stochastic matrix to a column vector, This coeffic ient underlies his ergodicity arguments, and his proof of the Weak Law .