Anrei Andreevich Markov

 

 

Andrei Andreevich Markov was born June 2, 1856 in Ryazan, Russia. In his early years, he attended school in Petersburg and was a poor student in everything but mathematics. He was somewhat of a rebel, and this quality stayed with him into adulthood, causing many problems with his government and peers.

He was a student under P. L. Chebyshev at the Petersburg University in 1874, and completed his studies there in 1878. He received a gold medal from the university and was asked to stay and become an academic by profession. When Chebyshev left the university, Markov taught his probability courses.

Markov was elected to be a member of the mathematical "school" founded by Chebyshev, the St. Petersburg Academy of Science, in 1886. He became a full member by 1896 and retired from the University (although he continued to teach) in 1905. He was also one of the early mathematicians who were always seeking the practical uses for statistics and probability, and took part in debates about the running of certain departments of the government and also teaching math in high schools.

Markov was one of Chebyshevís most famous disciples and his ideas were always trying to represent probability as an exact and practical mathematical science, even before R. A. Fisher. He and one of Chebyshevís other great students, Liapunov, were very focused on their mentorsí ideas. Markov especially focused on the method of movements. His introduction of the Markov chain as a model for the study of random variables made huge amounts of research possible in stochastic processes [ a stochastic process is a family or a collection of random variables indexed by a parameter-also called a chance or random process. The common indexes used are time and space to represent random phenomena.] He mostly confined his work to investigating the Weak Law of Large numbers (WLLN) and the Central Limit Theorem. His motivation for the writing of his papers involving the Markov chains was first, to show that Chebyshevís approach to extending the Weak Law of Large numbers to sums of dependent random variables could be taken even further. Second, and probably more applicable, is an animosity between Markov and P. A. Nekrasov. In 1902, Nekrasov said that not only would "pairwise independence" yield the WLLN according to Chebychevís deductions, but also he claimed without much proof and wrongly that it was not only sufficient but necessary for the WLLN to hold. Markov, of course, refuted this argument (and correctly) in his papers, and thereby made a lifelong adversary out of Nekrasov. In doing all this, he uses his self-named Markov chains as part of the processes.

A practical use for his mathematics was found in his use of his chains to model the alteration of vowels and consonants in Russian literary works. He also wrote a statistics and probability textbook, one of the best in its time. His work influenced many other famous mathematicians and statisticians, including S. N. Bernstien, V. I. Romanovsky, and Jerzy Neyman (who then took statistics to a new and more practical level). After contributing a great deal to number theory, analysis, calculus of finite differences, probability theory (with the Markov chains), and statistics, he died in Petrograd (formerly St. Petersburg, now Leningrad), U. S. S. R., on July 20, 1922.