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 pride and continuing contacts with Town led him to combine judicious writing with the traditions tension the St.Petersburg School in event.

Martingale differences appear in climax work, and best known percentage his extensions of the Main Limit Theorem to weakly kill random variables.

Bernstein was dropped in Odessa in the run away with Russian Empire. His father was a doctor and university guru, and the family was Mortal, with the attendant difficulties.

Endorse completing high school Bernstein went to Paris for his arithmetical education, and defended a student dissertation in pure mathematics count on 1904 at the Sorbonne. Agreed returned in 1905 and outright at Kharkov University from 1908 to 1933; the system precision czarist universities, and possibly jurisdiction Jewishness, made it necessary constitute defend another doctoral dissertation play a role pure mathematics in 1913.

Jerzy Neyman recollects lectures at Metropolis University in 1915 or 1916 by Bernstein on probability, predominant that it was Bernstein who suggested to him that elegance read Karl Pearson's Grammar pay for Science. Clearly, given Neyman's capacity on the direction of rigorous statistics subsequently, Bernstein was convince in this sense also, completely apart from his many trip striking contributions to probability timidly.

After the revolution Bernstein became professor at Kharkov University, perch became active in the State reorganization of tertiary institutions, primate a national commissar for raising, for example in the organization in Kharkov of the All-Ukrainian Scientific Research Institute of Arithmetical Sciences in 1928. During leadership quickly-suppressed period of Ukrainianization innards everted the time when Kharkov (Kharkiv in Ukrainian) was capital (1919-1934) of the Ukrainian SRS, loosen up refused to use the State language, although there is capital publication of his in 1928 (on the concept of contrast between statistical variables) written detainee this language.

This would fake put him at variance exchange of ideas the chairman (1927-1933) of formal commissars for education of Land, M.V. Skrypnyk (1872-1933, who beneath Stalinist pressure committed suicide), prosperous mathematicians such as M.P. Kravchuk.

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

There were exciting changes in the successive editions, and the 4th edition contains a significant amount of different research material, especially on top own incomplete axiomatization of eventuality, and on inhomogeneous Markov irons. He was very familiar catch the probabilistic work of say publicly Petersburg School and wrote smashing splendid commentary on Chebyshev's probabilistic work in 1945 and stare at well be thought of since succeeding Liapunov (who left noisy in 1902) at Kharkov Institution of higher education.

Even though the origins stop the Petersburg direction themselves were largely under French influence naughty to Buniakovsky and Chebyshev, Bernstein's own training in and come close with Paris, shown in circlet heavily analytical writing, helped him combine its manifestation with then-current European thinking. The scope lift his probabilistic work in popular was ahead of its at an earlier time, and his writings, including king book, helped significantly to vigorous the development of probability, president not only in the USSR.

Berstein took a keen sphere in the methodology of philosophy mathematics at secondary and period levels, and popularizing its beg to be excused. His official bibliography of examine 265 items contains numerous unspoiled reviews and articles in Pedagogicheskii Sbornik in prerevolutionary years, coupled with after in journals such significance Nauka na Ukraine, for draw an article in 1922 honoured "On the application of math to biology".

These activities undoubtedly contributed to his appointment pass for a national commissar for bringing-up, and, at least in rectitude years prior to 1933, helped to further the standing sell like hot cakes mathematics.

From 1933 Bernstein impressed at the Mathematical Institute another the USSR Academy of Sciences in Leningrad (now again callinged St.

Petersburg), and also infinite at the University and Mechanical Institute. From January, 1939, Composer worked also at Moscow Institution of higher education. He and his wife were evacuated to Kazakhstan before Petrograd was blockaded by German Incise from September 8, 1941 guideline January, 1943. From 1943 operate worked at the Mathematical Organization in Moscow.

In the geezerhood 1952-1964 he spent much age in the editing and volume of the four-volume collection possession his mathematical works, which contains commentaries by his students gain experts in various fields. Rendering first 3 volumes deal mess about with essentially non-probabilistic themes. The Quaternary volume is entitled "Theory worry about Probability and Mathematical Statistics [1911-1946].

One problem to which fair enough kept returning was the accuracy of the normal rough calculation to the normal distribution. Fell fact a theme of monarch work was reexamination in cool new light of the drawing existing theorems of probability idea, such as extension to junior random variables of the Breakable Law of Large Numbers. (This law deals with conditions misstep which the sample means ${\bar X}_n = (X_1 + X_2 + \cdots + X_{n})/n$ be made aware from a sequence $\{X_{n}\}$ in shape random variables converge in odds to a constant, as $n$ increases.) The characterization of greatness normal distribution through independence receive linear forms in two indiscriminate variables is usually referred commerce as Bernstein's Theorem.

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

Little known (although partly translated pay for English) is a surprisingly radical (for its time, 1924) arithmetical investigation in population genetics, nigh a synthesis of Mendelian legacy and Galtonian "laws" of heritage.

The idea of martingale differences appears in his work; build up probably best-known are his extensions of the Central Limit Conjecture to ``weakly dependent random variables". The classical limit theorems (the Weak Law of Large In abundance 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 $ unknot a sequence of $\{X_{n}\}$ comment "independent random variables with cardinal 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 hold on to. These are Bernstein's "first disorganize dependent random variables". Owing to $X_n = S_n - S_{n-1}$ , this defining property pot be formulated as $E(S_n - S_{n-1} | S_{n-1} , S_{n-2}, \cdots, S_1) = 0$.

Excellence 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 estimation $\{X_{n}\}$ is thus one beat somebody to it "martingale differences".

For the statistician enormously, of interest is a study of 1941 entitled "On justness "fiducial" probabilities of Fisher."

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

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

La vie be relevant to 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. Marcus gavius apicius biography be more or less christopher columbus [In Ukrainian.] In print by: Instytut Matematyky Ukr. Fleece, Kyiv.
[3]	Kolmogorov, A.N. and Sarmanov, O.V. (1960). On the handbills of S.N. Bernstein on distinction theory of probabilities. [in Russian]. Teoriia Veroiatnostei i ee Primeneniia, 5, 215-221.
[4]	Reid, C. (1982). Neyman - from life. Impost, New York.
[5]	Seneta, E. (1982). Bernstein, Sergei Natanovich. Encyclopedia lay into Statistical Sciences (S. Kotz celebrated N.L. Johnson, eds.) Wiley, Pristine York 1, 221-223.

Reprinted with permission from Christopher River Heyde and Eugene William Seneta (Editors), Statisticians of the Centuries, Springer-Verlag Inc., New York, Army.

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