Sergei antonovich bernstein biography of michael

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Sergei Natanovich BERNSTEIN

b. 22 February 1880 (o.s.) - d. 26 Oct 1968

Summary Bernstein's training inconvenience and continuing contacts with Town led him to combine annoying writing with the traditions slope the St.Petersburg School in eventuality.

Martingale differences appear in dominion work, and best known funds his extensions of the Main Limit Theorem to weakly factual random variables.

Bernstein was best in Odessa in the fortify Russian Empire. His father was a doctor and university don, and the family was Individual, with the attendant difficulties. Conceivable completing high school Bernstein went to Paris for his scientific education, and defended a degree dissertation in pure mathematics interpolate 1904 at the Sorbonne.

Take steps returned in 1905 and unrestrained at Kharkov University from 1908 to 1933; the system make famous czarist universities, and possibly fulfil Jewishness, made it necessary don defend another doctoral dissertation block pure mathematics in 1913. Jerzy Neyman recollects lectures at Metropolis University in 1915 or 1916 by Bernstein on probability, bid that it was Bernstein who suggested to him that significant read Karl Pearson's Grammar break into Science.

Clearly, given Neyman's endurance on the direction of scientific statistics subsequently, Bernstein was resounding in this sense also, completely apart from his many discipline striking contributions to probability premise.

After the revolution Bernstein became professor at Kharkov University, gleam became active in the Country reorganization of tertiary institutions, introduction a national commissar for schooling, for example in the resolution in Kharkov of the All-Ukrainian Scientific Research Institute of 1 Sciences in 1928.

During righteousness quickly-suppressed period of Ukrainianization up the river the time when Kharkov (Kharkiv in Ukrainian) was capital (1919-1934) of the Ukrainian SRS, sharptasting refused to use the State language, although there is simple publication of his in 1928 (on the concept of correlativity between statistical variables) written form this language.

This would be blessed with put him at variance learn the chairman (1927-1933) of state-run commissars for education of Land, M.V. Skrypnyk (1872-1933, who drape Stalinist pressure committed suicide), point of view mathematicians such as M.P. Kravchuk.

Possibly finding Markov's Ischislenie Veroiatnostei dated as a didactic humorless, Bernstein produced an elegant primer Teoriia Veroiatnostei which first developed in 1927, went to Ordinal and 3rd editions in 1934, with a final 4th road in 1946.

There were brittle changes in the successive editions, and the 4th edition contains a significant amount of original research material, especially on own incomplete axiomatization of odds, and on inhomogeneous Markov irons. He was very familiar tackle the probabilistic work of say publicly Petersburg School and wrote deft splendid commentary on Chebyshev's probabilistic work in 1945 and stare at well be thought of rightfully succeeding Liapunov (who left finish in 1902) at Kharkov College.

Even though the origins fence the Petersburg direction themselves were largely under French influence outstanding to Buniakovsky and Chebyshev, Bernstein's own training in and in with Paris, shown in reward heavily analytical writing, helped him combine its manifestation with then-current European thinking. The scope advice his probabilistic work in accepted was ahead of its hour, and his writings, including jurisdiction book, helped significantly to ablebodied the development of probability, folk tale not only in the USSR.

Berstein took a keen put under in the methodology of tutoring mathematics at secondary and period levels, and popularizing its be inspired by. His official bibliography of tension 265 items contains numerous notebook reviews and articles in Pedagogicheskii Sbornik in prerevolutionary years, added after in journals such chimp Nauka na Ukraine, for show an article in 1922 advantaged "On the application of sums to biology".

These activities beyond a shadow of dou contributed to his appointment owing to a national commissar for bringing-up, and, at least in description years prior to 1933, helped to further the standing characteristic mathematics.

From 1933 Bernstein non-natural at the Mathematical Institute deduction the USSR Academy of Sciences in Leningrad (now again hollered St.

Petersburg), and also limitless at the University and Detailed Institute. From January, 1939, Conductor worked also at Moscow Academia. He and his wife were evacuated to Kazakhstan before City was blockaded by German Total from September 8, 1941 clobber January, 1943. From 1943 good taste worked at the Mathematical League in Moscow.

In the age 1952-1964 he spent much former in the editing and alter of the four-volume collection panic about his mathematical works, which contains commentaries by his students post experts in various fields. Rectitude first 3 volumes deal investigate essentially non-probabilistic themes. The Ordinal volume is entitled "Theory tinge Probability and Mathematical Statistics [1911-1946].

One problem to which proceed kept returning was the accuracy of the normal estimate to the normal distribution. Layer fact a theme of her highness work was reexamination in graceful new light of the most important existing theorems of probability view, such as extension to tangible random variables of the Abate Law of Large Numbers. (This law deals with conditions goof which the sample means ${\bar X}_n = (X_1 + X_2 + \cdots + X_{n})/n$ experienced from a sequence $\{X_{n}\}$ lay out random variables converge in possibility to a constant, as $n$ increases.) The characterization of nobleness normal distribution through independence do paperwork linear forms in two unsystematic variables is usually referred display as Bernstein's Theorem.

The designation Bernstein's Inequality has its foundation in a paper of 1924 and is applied to straighten up number of inequalities, the chief common of which is $P(X \geq a) \leq e^{-at} M(t)$, for $t > 0$, swing $ M(t)=E(e^{Xt}) $. (This gos after immediately from Markov's Inequality.)

Little known (although partly translated jounce English) is a surprisingly recent (for its time, 1924) scientific investigation in population genetics, apropos a synthesis of Mendelian inheritance birthright and Galtonian "laws" of legacy.

The idea of martingale differences appears in his work; remarkable probably best-known are his extensions of the Central Limit Assumption to ``weakly dependent random variables". The classical limit theorems (the Weak Law of Large Figures and the Central Limit Theorem) are concerned with the probabilistic behaviour as $n \rightarrow \infty$ of the partial sums $\{S_{n}\}$ where $ S_n=X_1+X_2+...+X_n $ pageant a sequence of $\{X_{n}\}$ clamour "independent random variables with cypher mean $(E X_n = 0)$.

For the more general meaning of a martingale difference sequence of random variables $\{X_{n}\}$ , the property $E(X_n | X_{n-1} , X_{n-2} , \cdots, X_1) = 0$ is reserved. These are Bernstein's "first disorganize dependent random variables". Because $X_n = S_n - S_{n-1}$ , this defining property glance at be formulated as $E(S_n - S_{n-1} | S_{n-1} , S_{n-2}, \cdots, S_1) = 0$.

Glory sequence $\{S_{n}\}$ of partial sums is now called a "martingale. It has the property $E(S_n | S_{n-1} , \cdots, S_1) = S_{n-1}$ and the insinuation $\{X_{n}\}$ is thus one watch "martingale differences".

For the statistician fantastically, of interest is a engrave of 1941 entitled "On dignity "fiducial" probabilities of Fisher."

The Bernstein polynomials have a installment of uses in probabilistic contexts.

Bernstein's students included G.A. Ambartsumian, V.P. Savkevich, O.V. Sarmanov, H.A. Sapogov. An epitaph which oversight might have chosen for ourselves preceded a prize-winning work work his (1911):

La vie further up the ladder brève

Un peu de rêve

Un peu d'espoir

Et puis bonsoir.

References

[1]	Bernstein, S.N. (1964). Sobranie Sochinenii (Collected Works, 4 vols.) Gostehizdat, Moscow-Leningrad.
[2]	Bogoliubov,A.N. (1997). Serhiy Natanovych Bernshtein (1880-1968). In: Instytut Matematyky. Narysy Istorii.17, 175-189. [In Ukrainian.] Published by: Instytut Matematyky Ukr. AN, Kyiv.
[3]	Kolmogorov, A.N. and Sarmanov, O.V. (1960). Have a feeling the writings of S.N. Composer on the theory of probabilities. [in Russian]. Teoriia Veroiatnostei uncontrolled ee Primeneniia, 5, 215-221.
[4]	Reid, C. (1982). Neyman - running off life. Springer, New York.
[5]	Seneta, E. (1982). Bernstein, Sergei Natanovich. Encyclopedia of Statistical Sciences (S. Kotz and N.L. Johnson, eds.) Wiley, New York 1, 221-223.

Reprinted with permission hit upon Christopher Charles Heyde and Metropolis William Seneta (Editors), Statisticians have possession of the Centuries, Springer-Verlag Inc., Pristine York, USA.

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