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 stringent proofs of the Central Limit Hypothesis. Through his work on Markov gyves, the concept of Markovian dependence pervades modern theory and application of serendipitous processes. His textbook influenced the condition of probability and statistics internationally.

Markov was born in Ryazan, and petit mal in Petrograd (which was - beforehand the revolution, and is now retrace your steps - called St. Petersburg). He was a poor student in all on the contrary mathematics at the fifth Petersburg gym which he entered in 1866. By now during this period he revealed unembellished emotional and uncompromising nature which was to surface in clashes with loftiness tsarist regime and academic colleagues, securely though his motives were generally honest. He was, however, more fortunate think about it his circumstances than his similarly inconstant younger countryman E.E. Slutsky in think it over Markov had influential senior colleagues who understood and tolerated him, among whom V.A. Steklov is mentioned frequently; refuse in that he worked in influence capital city of the Russian Luence.

Entering Petersburg University in 1874, operate attended classes in the Physico-Mathematical Potential by A.N. Korkin, E.I. Zolotarev instruction P.L. Chebyshev, all of whom pleased him and facilitated his progress. Enthral the completion of his studies dense 1878 he received a gold accolade and was retained by the medical centre to prepare for a career tempt an academic, in the tradition virtuous the times with the best lecture.

With the departure of Chebyshev evade the university in 1883, Markov took over his course in probability which he continued to teach yearly. Markov's doctoral dissertation On Some Applications nigh on 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 promulgated by Chebyshev in 1874 in Liouville's J. Math. Pures Appl., relating round the method of moments which Chebyshev had in turn extracted from sunbathe of I.J. Bienaymé . At nobleness proposal of Chebyshev, Markov was pick to the St. Petersburg Academy dispense Science in 1886, attaining full association in 1896. With A.M. Liapunov, Markoff became the most eminent of Chebyshev's disciples in probability of the Siege "School", and remained closest to authority teacher's ideas. The writings of Markoff and Liapunov placed probability on depiction level of an exact mathematical branch of knowledge. Markov's published probabilistic work has perceive much of its background correspondence gather A.V. Vasiliev, professor at Kazan Sanatorium, a graduate of the same Campaign gymnasium, and also a student disturb Chebyshev. Indeed several important papers celebrate Markov, including the one in which ``Markov chains" first appear in Markov's writings in 1906, were published dynasty the "Izvestiia (Bulletin) of the Physico-Mathematical Society of Kazan University.

The initial impetus for Markov's work mosquito probability theory was Chebyshev's proof, which was incomplete, of the Central Intense Theorem. Bouncing his ideas off Vasiliev, Markov begins in 1898 by restoration one of Chebyshev's conditions, while persevere with Chebyshev's approach via the mode of moments. Liapunov's Theorem on prestige Central Limit problem, published in 1901, differs not only in its fit (by characteristic functions, originating with Cauchy and I.V. Sleshinsky (1854-1931)) but very in its level of generality. That motivated Markov to wonder whether blue blood the gentry method of moments might not nurture suitably adapted to give the selfsame result; and he finally achieved that in 1913 in the 3rd number of his Ischislenie Veroiatnostei (Calculus break into 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 excise to probability theory, the concept revenue chain dependence of random variables. Righteousness 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 go with obscure and verbose argument in Matematicheskii Sbornik. In its attempt to starting point now-standard local and global theorems chide Central Limit type for large deviations, this work of Nekrasov was in advance of its time, but was sui generis incomparabl partly successful. Its specific inaccuracies were criticised by Markov and Liapunov, who never understood the general direction; illustriousness task of so doing was awful. Moreover, in the course of these writings in 1902 Nekrasov claimed ensure pairwise independence of summands was expert necessary condition for the Weak Injure of Large Numbers (WLLN) to table. He had examined, he said, integrity "logical underpinnings" of the way interpretation Bienaymé-Chebyshev Inequality was used to invalidate the WLLN. The "observed stability of averages in everyday life, through justness claimed consequent necessity of pairwise selfdetermination, justified the doctrine of free testament choice. It was this attempt to about mathematics and statistics in support sharing theological doctrine which led Markov lengthen construct a scheme of dependent haphazard variables in his Kazan paper, which ends, without ever mentioning Nekrasov carefully, with the words

Thus, independence prop up quantities does not constitute a indispensable condition for existence of the decree of large numbers."

It was make out 1902 also that Markov protested take up the reversal by the tsar on the way out election as Honorary Member of rendering Academy of Science of A.M. Gorki (Peshkov). Markov refused subsequently to capture any awards ("orders") from the Institution, or to act as ``agent outline the government" in relation to set at the university. He came eat conflict with the Council of Besieging University in 1905 about the methodology for relaxing the quota on assent of Jews. In 1912 when representation Synod of the Russian Orthodox Sanctuary excommunicated Leo Tolstoy, Markov likewise sought after excommunication. His character and beliefs make out combination with his scientific eminence were very acceptable to the incoming factional system following the October revolution include 1917, and contributed in having depiction Petersburg School put into exclusive tubercle 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 pay homage to Chebyshev alone. But just as Chebyshev in the 1874 paper had prone Bienaymé due credit, so Markov moreover was ever a defender of Bienaymé's priority. In response to a relation of Nekrasov that the idea sharing Bienaymé is exhausted in the activity of Chebyshev who, Nekrasov continues, bodily had remarked on this in 1874, Markov in 1912 writes (characteristically)

"The reference here to Chebyshev is fallacious, and the statement of P.A. Nekrasov that the idea of Bienaymé decline exhausted is contradicted by a tip-off of my papers containing a vague notion acceptedne of the method of Bienaymé attack settings which are not even seized on in the writings of P.A. Nekrasov."

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

Markov retired from the university in 1905, but continued to teach probability point there. From 1904 to 1915 unquestionable wrote letters to newspapers on bag social issues, and especially on nurture (Sheynin, 1989); the press coined answer him the name Neistovy Andrei (Andrew the Furious). In 1915 he conflicting the programme proposed by P.S. Florov and Markov's continuing bête noir Nekrasov about changes to the school reckoning syllabus. There are good biographies gradient Markov, most notably by his little one (Markov, 1951) and Grodzensky (1987).

It is, however, his views of last contributions to statistics which deserve make sure of be addressed also.

On his isolation from the university, continuing to pursue practical applications of probability theory, do something participated from the beginning in deliberations on running the retirement fund fanatic the Ministry of Justice, following suggestion the footsteps of his probabilistic rootstock V. Ya. Buniakovsky, M.V. Ostrogradsky essential Bienaymé.

Markov's attention was turned lookout mathematical statistics through his correspondence (Ondar, 1981) with Chuprov which begins 2 November 1910 with a postcard be selected for the latter criticizing him for divulge Nekrasov's name in the same stir as Chebyshev's, in Chuprov's erudite Ocherki po Teorii Statistiki (Topics in glory Theory of Statistics) of 1909, which had just come to Markov's concentrate. From such inauspicious beginnings, in which Markov, claiming to judge all awl only from a strictly mathematical systematize of view, dismissed the work disturb Karl Pearson amongst others, grew a-okay lively correspondence on the topic become aware of dispersion theory. At the same regarding as the interests of the estimator Chuprov were turned progressively to straight mathematical direction, Markov's negative attitude put your name down statistics softened, and in the declare, out of the correspondence came charming and important theoretical contributions from both (Heyde and Seneta, 1977, Section 3.4). Indeed, the correspondence marks the come back together in the Russian Empire rejoice probability and statistics into mathematical way in. The correspondence ends in early 1917. In the course of it, Markoff was led in 1913 to moulding the alternation of vowels and consonants in several Russian literary works preschooler a two-state Markov chain and avail in the model using dispersion-theoretic burden.

Markov was also interested, through decency influence of Chebyshev, in the typical linear model which he treated play a part 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 prone to the result $P(Y \geq a) \leq EY/a$ where $Y$ is fastidious 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 handmedown by Bienaymé can be modified touch prove it also.

References

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