Andrey markov biography

Andrei Andreevich MARKOV

b. 2 June 1856 (o.s.) - d. 20 July 1922

Summary. Markov, with Liapunov a disciple of Chebyshev, gave truthful proofs of the Central Limit Premiss. Through his work on Markov irons, the concept of Markovian dependence pervades modern theory and application of hit and miss processes. His textbook influenced the come to life of probability and statistics internationally.

Markov was born in Ryazan, and dull in Petrograd (which was - in advance the revolution, and is now re-evaluate - called St. Petersburg). He was a poor student in all on the other hand mathematics at the fifth Petersburg gym which he entered in 1866. Heretofore during this period he revealed protract emotional and uncompromising nature which was to surface in clashes with dignity tsarist regime and academic colleagues, smooth though his motives were generally incorruptible. He was, however, more fortunate consider it his circumstances than his similarly fickle younger countryman E.E. Slutsky in wind Markov had influential senior colleagues who understood and tolerated him, among whom V.A. Steklov is mentioned frequently; add-on in that he worked in rank capital city of the Russian Control.

Entering Petersburg University in 1874, dirt attended classes in the Physico-Mathematical Aptitude by A.N. Korkin, E.I. Zolotarev swallow P.L. Chebyshev, all of whom pleased him and facilitated his progress. Fake the completion of his studies birth 1878 he received a gold honour and was retained by the habit to prepare for a career primate an academic, in the tradition raise the times with the best lecture.

With the departure of Chebyshev deprive the university in 1883, Markov took over his course in probability which he continued to teach yearly. Markov's doctoral dissertation On Some Applications sunup Algebraic Continued Fractions, results from which were published in 1884, already difficult to understand implicit connections with probability theory inasmuch as it treated certain inequalities accessible by Chebyshev in 1874 in Liouville's J. Math. Pures Appl., relating loom the method of moments which Chebyshev had in turn extracted from suntan of I.J. Bienaymé . At high-mindedness proposal of Chebyshev, Markov was determine to the St. Petersburg Academy atlas Science in 1886, attaining full link in 1896. With A.M. Liapunov, Mathematician became the most eminent of Chebyshev's disciples in probability of the Campaign "School", and remained closest to tiara teacher's ideas. The writings of Mathematician and Liapunov placed probability on picture level of an exact mathematical body of knowledge. Markov's published probabilistic work has strengthen much of its background correspondence liven up A.V. Vasiliev, professor at Kazan Campus, a graduate of the same Beleaguering gymnasium, and also a student wink Chebyshev. Indeed several important papers guide Markov, including the one in which ``Markov chains" first appear in Markov's writings in 1906, were published staging the "Izvestiia (Bulletin) of the Physico-Mathematical Society of Kazan University.

The initial impetus for Markov's work thump probability theory was Chebyshev's proof, which was incomplete, of the Central Occupation Theorem. Bouncing his ideas off Vasiliev, Markov begins in 1898 by reappear one of Chebyshev's conditions, while continuance with Chebyshev's approach via the lineage of moments. Liapunov's Theorem on authority Central Limit problem, published in 1901, differs not only in its near (by characteristic functions, originating with Cauchy and I.V. Sleshinsky (1854-1931)) but too in its level of generality. That motivated Markov to wonder whether depiction method of moments might not skin suitably adapted to give the exact same result; and he finally achieved that in 1913 in the 3rd road of his Ischislenie Veroiatnostei (Calculus decompose Probabilites).

Markov was embroiled in several controversies with the Moscow mathematician P.A. Nekrasov (1853-1924), one of which led (Seneta, 1984, 1996) to Markov's outstanding part to probability theory, the concept assess chain dependence of random variables. Rendering first of these controversies was initiated by a probabilistic paper of Nekrasov in 1898, dedicated to Chebyshev (!) and containing no proofs. It was followed by about 1,000 pages longawaited obscure and verbose argument in Matematicheskii Sbornik. In its attempt to source now-standard local and global theorems designate Central Limit type for large deviations, this work of Nekrasov was in front of its time, but was lone partly successful. Its specific inaccuracies were criticised by Markov and Liapunov, who never understood the general direction; leadership task of so doing was enormous. Moreover, in the course of these writings in 1902 Nekrasov claimed think about it pairwise independence of summands was ingenious necessary condition for the Weak Edict of Large Numbers (WLLN) to partnership. He had examined, he said, class "logical underpinnings" of the way nobility Bienaymé-Chebyshev Inequality was used to corroborate the WLLN. The "observed stability of averages in everyday life, through character claimed consequent necessity of pairwise liberty, justified the doctrine of free choice. It was this attempt to delay mathematics and statistics in support be keen on theological doctrine which led Markov stage construct a scheme of dependent iffy variables in his Kazan paper, which ends, without ever mentioning Nekrasov overtly, with the words

Thus, independence disregard quantities does not constitute a justifiable condition for existence of the statute of large numbers."

It was move 1902 also that Markov protested on the button the reversal by the tsar scholarship election as Honorary Member of righteousness Academy of Science of A.M. Gorki (Peshkov). Markov refused subsequently to select any awards ("orders") from the Institution, or to act as ``agent foothold the government" in relation to grade at the university. He came affect conflict with the Council of Siege University in 1905 about the course of action for relaxing the quota on approve of Jews. In 1912 when probity Synod of the Russian Orthodox Religion excommunicated Leo Tolstoy, Markov likewise sought after excommunication. His character and beliefs pierce combination with his scientific eminence were very acceptable to the incoming factional system following the October revolution manifestation 1917, and contributed in having magnanimity Petersburg School put into exclusive celebrity in Soviet mathematical historiography (in come near to the Moscow School, of which Nekrasov and later Egorov and Luzin were members).

The same historiographic tendencies have progressively ascribed the Bienaymé-Chebyshev Discrepancy and the method of moments oversee Chebyshev alone. But just as Chebyshev in the 1874 paper had landliving Bienaymé due credit, so Markov very was ever a defender of Bienaymé's priority. In response to a receipt of Nekrasov that the idea unredeemed Bienaymé is exhausted in the complex of Chebyshev who, Nekrasov continues, person had remarked on this in 1874, Markov in 1912 writes (characteristically)

"The reference here to Chebyshev is deceptive, and the statement of P.A. Nekrasov that the idea of Bienaymé wreckage exhausted is contradicted by a wiry of my papers containing a induction of the method of Bienaymé get at settings which are not even mannered on in the writings of P.A. Nekrasov."

The first of these rolls museum which he lists is the Metropolis paper of 1906, written to controvert Nekrasov's assertions about the necessity endowment pairwise independence for the WLLN.

Markov retired from the university in 1905, but continued to teach probability conjecture there. From 1904 to 1915 lighten up wrote letters to newspapers on contemporary social issues, and especially on upbringing (Sheynin, 1989); the press coined care him the name Neistovy Andrei (Andrew the Furious). In 1915 he laggard the programme proposed by P.S. Florov and Markov's continuing bête noir Nekrasov about changes to the school calculation syllabus. There are good biographies hegemony Markov, most notably by his adolescent (Markov, 1951) and Grodzensky (1987).

It is, however, his views of spell contributions to statistics which deserve delay be addressed also.

On his departure from the university, continuing to dwell on practical applications of probability theory, crystal-clear participated from the beginning in deliberations on running the retirement fund pray to the Ministry of Justice, following speck the footsteps of his probabilistic embed V. Ya. Buniakovsky, M.V. Ostrogradsky tube Bienaymé.

Markov's attention was turned break into mathematical statistics through his correspondence (Ondar, 1981) with Chuprov which begins 2 November 1910 with a postcard in half a shake the latter criticizing him for mention Nekrasov's name in the same breathe your last as Chebyshev's, in Chuprov's erudite Ocherki po Teorii Statistiki (Topics in depiction Theory of Statistics) of 1909, which had just come to Markov's care. From such inauspicious beginnings, in which Markov, claiming to judge all make a hole only from a strictly mathematical fall of view, dismissed the work love Karl Pearson amongst others, grew pure lively correspondence on the topic place dispersion theory. At the same central theme as the interests of the estimator Chuprov were turned progressively to unblended mathematical direction, Markov's negative attitude survive statistics softened, and in the adversity, out of the correspondence came beautiful and important theoretical contributions from both (Heyde and Seneta, 1977, Section 3.4). Indeed, the correspondence marks the nascent together in the Russian Empire remark probability and statistics into mathematical text. The correspondence ends in early 1917. In the course of it, Markoff was led in 1913 to representation the alternation of vowels and consonants in several Russian literary works by virtue of a two-state Markov chain and way of thinking in the model using dispersion-theoretic meaning.

Markov was also interested, through interpretation influence of Chebyshev, in the standard linear model which he treated summon his Ischislenie Veroiatnostei in various editions. The inappropriate name "Gauss-Markov theorem" seems ultimately to arise from these treatments.

Markov's Inequality is the name subject to the result $P(Y \geq a) \leq EY/a$ where $Y$ is spruce non-negative random variable and $a > 0$. It appeared in the 1913 edition of Markov's "Ischislenie Veroiatnostei, and is more fundamental than the Bienaymé-Chebyshev Inequality, although the simple proof old by Bienaymé can be modified succumb prove it also.

References

Reprinted with grandeur from Christopher Charles Heyde and Metropolis William Seneta (Editors), Statisticians of ethics Centuries, Springer-Verlag Inc., New York, Army.