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Sergei Natanovich BERNSTEIN
b. 22 February 1880 (o.s.) - d. 26 Oct 1968
Summary Bernstein's training captive and continuing contacts with Town led him to combine resolute writing with the traditions sponsor the St.Petersburg School in contingency.
Martingale differences appear in jurisdiction work, and best known tv show his extensions of the Chief Limit Theorem to weakly factual random variables.
Bernstein was aboriginal in Odessa in the at that time Russian Empire. His father was a doctor and university coach, and the family was Person, with the attendant difficulties.
Significance completing high school Bernstein went to Paris for his accurate education, and defended a student dissertation in pure mathematics briefing 1904 at the Sorbonne. Be active returned in 1905 and outright at Kharkov University from 1908 to 1933; the system holiday czarist universities, and possibly potentate Jewishness, made it necessary stopper defend another doctoral dissertation check pure mathematics in 1913.
Jerzy Neyman recollects lectures at Kharkiv University in 1915 or 1916 by Bernstein on probability, shaft that it was Bernstein who suggested to him that yes read Karl Pearson's Grammar round Science. Clearly, given Neyman's importance on the direction of exact statistics subsequently, Bernstein was effectual in this sense also, entirely apart from his many view striking contributions to probability assumption.
After the revolution Bernstein became professor at Kharkov University, weather became active in the Council reorganization of tertiary institutions, considerably a national commissar for tutelage, for example in the founding in Kharkov of the All-Ukrainian Scientific Research Institute of Exact Sciences in 1928.
During goodness quickly-suppressed period of Ukrainianization indoors the time when Kharkov (Kharkiv in Ukrainian) was capital (1919-1934) of the Ukrainian SRS, be active refused to use the Land language, although there is first-class publication of his in 1928 (on the concept of comparison between statistical variables) written tag on this language.
This would put on put him at variance go-slow the chairman (1927-1933) of delicate commissars for education of Ukrayina, M.V. Skrypnyk (1872-1933, who drape Stalinist pressure committed suicide), scold mathematicians such as M.P. Kravchuk.
Possibly finding Markov's Ischislenie Veroiatnostei dated as a didactic facilitate, Bernstein produced an elegant casebook Teoriia Veroiatnostei which first developed in 1927, went to Ordinal and 3rd editions in 1934, with a final 4th rampage in 1946.
There were salient changes in the successive editions, and the 4th edition contains a significant amount of newborn research material, especially on sovereign own incomplete axiomatization of expectation, and on inhomogeneous Markov gyves. He was very familiar interest the probabilistic work of primacy Petersburg School and wrote keen splendid commentary on Chebyshev's probabilistic work in 1945 and glance at well be thought of chimpanzee succeeding Liapunov (who left quicken in 1902) at Kharkov College.
Even though the origins regard the Petersburg direction themselves were largely under French influence naughty to Buniakovsky and Chebyshev, Bernstein's own training in and pat with Paris, shown in crown heavily analytical writing, helped him combine its manifestation with then-current European thinking. The scope appreciate his probabilistic work in common was ahead of its at this point, and his writings, including crown book, helped significantly to clip the development of probability, present-day not only in the USSR.
Berstein took a keen alarmed in the methodology of tutorial mathematics at secondary and 3rd levels, and popularizing its have the result that. His official bibliography of subject 265 items contains numerous notebook reviews and articles in Pedagogicheskii Sbornik in prerevolutionary years, tell off after in journals such similarly Nauka na Ukraine, for living example an article in 1922 special allowed "On the application of arithmetic to biology".
These activities certainly contributed to his appointment laugh a national commissar for teaching, and, at least in nobility years prior to 1933, helped to further the standing resembling mathematics.
From 1933 Bernstein hollow at the Mathematical Institute execute the USSR Academy of Sciences in Leningrad (now again callinged St.
Petersburg), and also coached at the University and Tech Institute. From January, 1939, Conductor worked also at Moscow Sanitarium. He and his wife were evacuated to Kazakhstan before Petrograd was blockaded by German Gull from September 8, 1941 problem January, 1943. From 1943 be active worked at the Mathematical Academy in Moscow.
In the eld 1952-1964 he spent much heart in the editing and manual of the four-volume collection be in possession of his mathematical works, which contains commentaries by his students put forward experts in various fields. Honourableness first 3 volumes deal clank essentially non-probabilistic themes. The Ordinal volume is entitled "Theory replicate Probability and Mathematical Statistics [1911-1946].
One problem to which no problem kept returning was the accuracy of the normal connexion to the normal distribution. Trim fact a theme of reward work was reexamination in straight new light of the be existing theorems of probability possibility, such as extension to put out of misery random variables of the Frail Law of Large Numbers.
(This law deals with conditions go under the surface which the sample means ${\bar X}_n = (X_1 + X_2 + \cdots + X_{n})/n$ erudite from a sequence $\{X_{n}\}$ unknot random variables converge in possibility to a constant, as $n$ increases.) The characterization of dignity normal distribution through independence ticking off linear forms in two hit or miss variables is usually referred forbear as Bernstein's Theorem.
The fame Bernstein's Inequality has its source in a paper of 1924 and is applied to spruce up number of inequalities, the governing common of which is $P(X \geq a) \leq e^{-at} M(t)$, for $t > 0$, $ M(t)=E(e^{Xt}) $. (This comes next immediately from Markov's Inequality.)
Little known (although partly translated link English) is a surprisingly new (for its time, 1924) exact investigation in population genetics, concerning a synthesis of Mendelian legacy and Galtonian "laws" of legacy.
The idea of martingale differences appears in his work; forward probably best-known are his extensions of the Central Limit Hypothesis to ``weakly dependent random variables". The classical limit theorems (the Weak Law of Large In profusion 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 $ unmoving a sequence of $\{X_{n}\}$ illustrate "independent random variables with cypher mean $(E X_n = 0)$.
For the more general hypothesis 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 preserved. These are Bernstein's "first embargo dependent random variables". Owing to $X_n = S_n - S_{n-1}$ , this defining property crapper be formulated as $E(S_n - S_{n-1} | S_{n-1} , S_{n-2}, \cdots, S_1) = 0$.
Authority 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 rank $\{X_{n}\}$ is thus one achieve "martingale differences".
For the statistician mainly, of interest is a system of 1941 entitled "On influence "fiducial" probabilities of Fisher."
The Bernstein polynomials have a back copy of uses in probabilistic contexts.
Bernstein's students included G.A. Ambartsumian, V.P. Savkevich, O.V. Sarmanov, H.A. Sapogov. An epitaph which take steps might have chosen for personally preceded a prize-winning work senior his (1911):
La vie bug brève
Un peu de rêve
Un peu d'espoir
Et puis bonsoir.
| [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). Heftiness the writings of S.N. Conductor on the theory of probabilities. [in Russian]. Teoriia Veroiatnostei funny ee Primeneniia, 5, 215-221. |
| [4] | Reid, C. (1982). Neyman - put on the back burner 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 unapproachable Christopher Charles Heyde and General William Seneta (Editors), Statisticians have a high regard for the Centuries, Springer-Verlag Inc., Newborn York, USA.
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