Markov, Andrey Andreyevich

Markov, Andrey Andreyevich

▪ Russian mathematician
born June 14, 1856, Ryazan, Russia
died July 20, 1922, Petrograd [now St. Petersburg]

      Russian mathematician who helped to develop the theory of stochastic processes (stochastic process), especially those called Markov chains (Markov process). Based on the study of the probability of mutually dependent events, his work has been developed and widely applied in the biological and social sciences.

      As a child Markov had health problems and used crutches until he was 10 years old. In 1874 he enrolled at the University of St. Petersburg (now St. Petersburg State University (Saint Petersburg State University)), where he earned a bachelor's degree (1878), a master's degree (1880), and a doctorate (1884). In 1883, as his station in life improved, he married his childhood sweetheart, the daughter of the owner of the estate that his father managed. Markov became a professor at St. Petersburg in 1886 and a member of the Russian Academy of Sciences (Sciences, Academy of) in 1896. Although he officially retired in 1905, he continued to teach probability courses at the university almost to his deathbed.

      While his early work was devoted to number theory and analysis, after 1900 he was chiefly occupied with probability theory. As early as 1812 the French mathematician Pierre-Simon Laplace (Laplace, Pierre-Simon, marquis de) had formulated the first central limit theorem, which states, roughly speaking, that probabilities for almost all independent and identically distributed random variables converge rapidly (with sample size) to the area under an exponential function. (See also normal distribution.) In 1887 Markov's teacher Pafnuty Chebyshev (Chebyshev, Pafnuty Lvovich) outlined a proof of a generalized central limit theorem. Using a different approach, Chebyshev's student Aleksandr Lyapunov proved the theorem under weakened hypotheses in 1901. Eight years later Markov succeeded in proving the general result rigorously using Chebyshev's method. While working on this problem, he extended both the law of large numbers (which states that the observed distribution approaches the expected distribution with increasing sample size) and the central limit theorem to certain sequences of dependent random variables forming special classes of what are now known as Markov chains (Markov process). These chains of random variables have found numerous applications in modern physics. One of the earliest applications was to describe Brownian motion, the small, random fluctuations or jiggling of small particles in suspension. Another frequent application is to the study of fluctuations in stock prices, generally referred to as random walks (random walk).

* * *


Universalium. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Markov , Andrey Andreyevich — (1856–1922) Russian mathematician Born at Ryazan in Russia, Markov studied at the University of St. Petersburg and later held a variety of teaching posts at the same university, eventually becoming a professor in 1893. He was an extremely… …   Scientists

  • Markov process — Statistics. a process in which future values of a random variable are statistically determined by present events and dependent only on the event immediately preceding. Also, Markoff process. [1935 40; after Russian mathematician Andrei Andreevich …   Universalium

  • Andrey Markov (Soviet mathematician) — Andrey Andreyevich Markov Jr. ( ru. #x410; #x43D; #x434; #x440; #x435; #x439; #x410; #x43D; #x434; #x440; #x435; #x435; #x432; #x438; #x447; #x41C; #x430; #x440; #x43A; #x43E; #x432;) (September 22, 1903 October 11, 1979) was a Soviet… …   Wikipedia

  • Andrey Markov — For other people named Andrey Markov, see Andrey Markov (disambiguation). Andrey (Andrei) Andreyevich Markov Born June 14, 1856( …   Wikipedia

  • Andréi Márkov — Andréi Márkov. Andréi Andréyevich Márkov (Андрей Андреевич Марков) (14 de junio de 1856 20 de julio de 1922) fue un matemático ruso conocido por sus trabajos en la teoría de los números y la teoría de probabilidades. Márkov nació en Riazán, Rusia …   Wikipedia Español

  • probability theory — Math., Statistics. the theory of analyzing and making statements concerning the probability of the occurrence of uncertain events. Cf. probability (def. 4). [1830 40] * * * Branch of mathematics that deals with analysis of random events.… …   Universalium

  • St. Petersburg Mathematical Society — The St. Petersburg Mathematical Society is a society of St. Petersburg mathematicians. It was dissolved and subsequently revived twice, each time changing its name: * St. Petersburg Mathematical Society (1890 1905) * Petrograd Physical and… …   Wikipedia

  • List of Russians — This is a list of people associated with Imperial Russia, the Soviet Union, and Russia of today. For a long time Russia has been a multinational country, and many people of different ethnicity contributed to its culture, to its glory, and to its… …   Wikipedia

  • Russian literature — Introduction       the body of written works produced in the Russian language, beginning with the Christianization of Kievan Rus in the late 10th century.       The unusual shape of Russian literary history has been the source of numerous… …   Universalium

  • List of assassinated people — This is a list of persons who were assassinated; that is, important people who were murdered, usually for ideological or political reasons. This list does not include executed persons. TOCright Assassinations in Africa Algeria *Hiempsal, (117 BC) …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”