Andrey Markov

For other people named Andrey Markov, see Andrey Markov (disambiguation).

Andrei Andreyevich Markov
Born	(1856-06-14)14 June 1856 N.S. Ryazan, Russian Empire
Died	20 July 1922(1922-07-20) (aged 66) Petrograd, Russian SFSR
Nationality	Russian
Alma mater	St. Petersburg University
Known for	{{collapsible list|title= | Markov chain Markov process stochastic processes Markov chain Additive Markov chain Absorbing Markov chain Nearly completely decomposable Markov chain Quantum Markov chain Telescoping Markov chain Examples of Markov chains Markov model Markov renewal process Markov chain mixing time Markov kernel Piecewise-deterministic Markov process Markovian arrival process Markov strategy Markov information source Hidden Markov model Markov chain Monte Carlo Reversible-jump Markov chain Monte Carlo Markov chain geostatistics Maximum-entropy Markov model Markovian discrimination Markov decision process Markov chain Markov reward model Markov switching multifractal Markov chain approximation method Markov logic network Markov chain approximation method Markov random field Lempel–Ziv–Markov chain algorithm Layered hidden Markov model Markov partition Partially observable Markov decision process Markov odometer Causal Markov condition Markov Reward Model Checker Dynamics of Markovian particles Markov perfect equilibrium (game theory) Markov's inequality Markov brothers' inequality Chebyshev–Markov–Stieltjes inequalities Markov–Krein theorem Gauss–Markov theorem Gauss–Markov process Dynamic Markov compression Markov algorithm Markov spectrum in [[Diophantine equations[[ Markov number (Diophantine equations) Markov–Kakutani fixed-point theorem Riesz–Markov–Kakutani representation theorem Markov theorem on braids Markov's principle Markov (crater) 27514 Markov, a main-belt asteroid Semi-Markov model}}
Children	Andrey Markov Jr.
Scientific career
Fields	Mathematician
Institutions	St. Petersburg University
Doctoral advisor	Pafnuty Chebyshev
Doctoral students	Abram Besicovitch Nikolai Günther Veniamin Kagan V. I. Romanovsky Jacob Tamarkin J. V. Uspensky Georgy Voronoy

Andrey Andreyevich Markov (1856 – 1922) was a Russian mathematician best known for his work on stochastic processes. A primary subject of his research later became known as Markov chains and Markov processes.

Markov and his younger brother Vladimir Andreevich Markov (1871–1897) proved the Markov brothers' inequality. His son, another Andrei Andreevich Markov (1903–1979), was also a notable mathematician, making contributions to constructive mathematics and recursive function theory. He is widely regarded as one of the foremost mathematicians of the 19th century.

Biography

Andrey Markov was born on 14 June 1856 in Russia. He attended Petersburg Grammar, where he was seen as a rebellious student by a select few teachers. In his academics he performed poorly in most subjects other than mathematics. Later in life he attended Petersburg University; among his teachers were Yulian Sokhotski (differential calculus, higher algebra), Konstantin Posse (analytic geometry), Yegor Zolotarev (integral calculus), Pafnuty Chebyshev (number theory and probability theory), Aleksandr Korkin (ordinary and partial differential equations), Mikhail Okatov (mechanism theory), Osip Somov (mechanics), and Nikolai Budaev (descriptive and higher geometry). He completed his studies at the University and was later asked if he would like to stay and have a career as a Mathematician. He later taught at high schools and continued his own mathematical studies. In this time he found a practical use for his mathematical skills. He figured out that he could use chains to model the alliteration of vowels and consonants in Russian literature. He also contributed to many other mathematical aspects in his time. He died at age 66 on 20 July 1922.

Timeline

In 1877, Markov was awarded a gold medal for his outstanding solution of the problem

About Integration of Differential Equations by Continued Fractions with an Application to the Equation $(1+x^{2}){\frac {dy}{dx}}=n(1+y^{2})$.

During the following year, he passed the candidate's examinations, and he remained at the university to prepare for a lecturer's position.

In April 1880, Markov defended his master's thesis "On the Binary Square Forms with Positive Determinant", which was encouraged by Aleksandr Korkin and Yegor Zolotarev. Four years later in 1884, he defended his doctoral thesis titled "On Certain Applications of the Algebraic Continuous Fractions".

His pedagogical work began after the defense of his master's thesis in autumn 1880. As a privatdozent he lectured on differential and integral calculus. Later he lectured alternately on "introduction to analysis", probability theory (succeeding Chebyshev, who had left the university in 1882) and the calculus of differences. From 1895 through 1905 he also lectured in differential calculus.

Markov in 1886

One year after the defense of his doctoral thesis, Markov was appointed extraordinary professor (1886) and in the same year he was elected adjunct to the Academy of Sciences. In 1890, after the death of Viktor Bunyakovsky, Markov became an extraordinary member of the academy. His promotion to an ordinary professor of St. Petersburg University followed in the fall of 1894.

In 1896, Markov was elected an ordinary member of the academy as the successor of Chebyshev. In 1905, he was appointed merited professor and was granted the right to retire, which he did immediately. Until 1910, however, he continued to lecture in the calculus of differences.

In connection with student riots in 1908, professors and lecturers of St. Petersburg University were ordered to monitor their students. Markov refused to accept this decree, and he wrote an explanation in which he declined to be an "agent of the governance". Markov was removed from further teaching duties at St. Petersburg University, and hence he decided to retire from the university.

Markov was an atheist. In 1912 he protested Leo Tolstoy's excommunication from the Russian Orthodox Church by requesting his own excommunication. The Church complied with his request.

Markov's headstone

In 1913, the council of St. Petersburg elected nine scientists honorary members of the university. Markov was among them, but his election was not affirmed by the minister of education. The affirmation only occurred four years later, after the February Revolution in 1917. Markov then resumed his teaching activities and lectured on probability theory and the calculus of differences until his death in 1922.

See also

• Chebyshev–Markov–Stieltjes inequalities
• Gauss–Markov theorem
• Gauss–Markov process
• Hidden Markov model
• Markov blanket
• Markov chain
• Markov decision process
• Markov's inequality
• Markov information source
• Markov network
• Markov number
• Markov property
• Markov process
• Stochastic matrix (also known as Markov matrix)
• Subjunctive possibility

Further reading

• Karl-Georg Steffens (28 July 2007). The History of Approximation Theory: From Euler to Bernstein. Springer Science & Business Media. pp. 98–105. ISBN 978-0-8176-4475-8.
• А. А. Марков. "Распространение закона больших чисел на величины, зависящие друг от друга". "Известия Физико-математического общества при Казанском университете", 2-я серия, том 15, ст. 135–156, 1906.
• A.A. Markov. "Extension of the limit theorems of probability theory to a sum of variables connected in a chain". reprinted in Appendix B of: R. Howard. Dynamic Probabilistic Systems, volume 1: Markov Chains. John Wiley and Sons, 1971.
• Pavlyk, Oleksandr (4 February 2013). "Centennial of Markov Chains". Wolfram Blog.

External links

• Andrei Andreyevich Markov at the Mathematics Genealogy Project
• Template:Worldcat id