7. Probability and Statistics Soviet Essays - Sheynin, Oscar

2. Gnedenko, B.V. (1949), On Lobachevsky’s work in the theory of probability. Istoriko-Matematich. Issledovania, vol. 2, pp. 129 – 136. (R)3. Ondar, Kh.O., Editor (1977, in Russian), The Correspondence between A.A. Markovand A.A. Chuprov. New York, 1981.4. Pólia, G. (1920), Über den zentralen Grenzwertsatz der Wahrschein-lichkeitsrechnungund das Momentproblem. Math. Z., Bd. 8, pp. 171 – 181.5. Sheynin, O. (1973), Finite random sums. Arch. Hist. Ex. Sci., vol. 9, pp. 275 – 305.6. --- (1990, in Russian), Chuprov. Göttingen, 1996.7. --- (1994), Chebyshev’s lectures on the theory of probability. Arch. Hist. Ex. Sci., vol.46, pp. 321 – 340.7. B.V. Gnedenko, A.N. Kolmogorov. Theory of probabilityUchenye Zapiski Moskovsk. Gosudarstven. Univ., No. 91, 1947, pp. 53 – 64[Introduction]The history of probability theory may be tentatively separated into four portions of time.[…]{The authors repeat here, almost word for word, Kolmogorov’s previous account of 1947also translated in this book.} The fourth period of the development of the theory begins inRussia with the works of Bernstein. […]The activities of the Moscow probability-theoretic school began somewhat later. It isnatural to consider that it originated with Khinchin’s works on the law of the iteratedlogarithm (in 1924) and Slutsky’s paper of 1925 on stochastic asymptotes and limits. Thedirection created by Bernstein along with the works of the Moscow school are stilldetermining the development of the Soviet probability theory. A number of new directionshave, however, appeared; the theory is successfully cultivated in an ever increasing numberof mathematical centers (Moscow, Leningrad, Tashkent, Kiev, Kharkov, etc), and the worksof the various directions become woven together ever more tightly 1 .Since the theory of probability has numerous diverse applications, scientific work oftentransforms here into solving separate and very special problems, sometimes demandingmasterly mathematical technique but introducing little innovation into the development of itsgeneral dominating ideas. Following the Chebyshev traditions, Soviet specialists alwaysattempted to isolate the main probability-theoretic patterns, deserving deep and exhaustivestudy out of this mess of separate applied problems. The limit theorems for sums ofindependent terms; Markov chains; general Markov processes; random functions and randomvector fields having distributions invariant with respect to some transformation group, – allthese classical or newer general subjects studied by Soviet mathematicians had originated asa result of thoroughly reasoning out the reduction of a large number of separate problemsfrom most diverse fields of natural sciences and technology to typical theoretical patterns.A simple formal classification is not at all sufficient for discovering these main theoreticalpatterns. Often only hard work on isolated problems makes it possible to reveal the fruitfulgeneral concept that enables to approach all of them by a single method. It is naturaltherefore that, at each stage of the development of science, which gradually appears out of amultitude of particular problems put forward for study from most various quarters, only apart of them is taken over by some established section of the general theory, whereas thesolution of a large number of problems is left to the devices of isolated amateurish methods.Such isolated problems should not at all be considered with contempt, especially if theirapplied importance is great. However, their solution could have only been included in ageneral review of the achievements of Soviet mathematicians during thirty years by listingthe titles of the appropriate contributions. We have therefore preferred to focus all ourattention on a small number of main directions, each of these being united by a sufficientlyclear dominating idea.