kniga 7 - Probability and Statistics 1 - Sheynin, Oscar

Cournot lemma as formulated by Chuprov 8 . Also in 1925, he published a fundamentalcontribution [13] where he defined and investigated the abovementioned notions, appliedthem for deriving necessary conditions for the law of large numbers, which he, in addition,generalized onto the multidimensional case. Later on this work became the basis of thetheory of stochastic functions.By 1926, Slutsky’s life in Kiev became very complicated. He did not master Ukrainian,and a compulsory demand of the time, that all the lectures be read in that language, made histeaching at Kiev higher academic institutions impossible. After hesitating for a long time,and being invited by the Central Statistical Directorate, he decided to move to Moscow.However, soon upon his arrival there, he was attracted by some scientific investigations (thestudy of cycles in the economy of capitalist countries) made at the Conjuncture Institute ofthe Ministry of Finance. E.E. became an active participant of this research, and, as usual,surrendered himself to it with all his passion. Here also, a great creative success lay ahead forhim. In March of that year he wrote to his wife:I am head over heels in the new work, am carried away by it. I am almostdefinitively sure about being lucky to arrive at a rather considerablefinding, to discover the secret of how are wavy oscillations originating by asource that, as it seems, had not been until now even suspected. Waves,known in physics, are engendered by forces of elasticity and rotatorymovements, but this does not yet explain those wavy movements that areobserved in social phenomena. I obtained waves by issuing from randomoscillations independent one from another and having no periodicitieswhen combining them in some definite way.The study of pseudo-periodic waves originating in series, whose terms are correlativelyconnected with each other, led Slutsky to a new important subject, to the errors of thecoefficients of correlation between series of that type. In both his investigations, he appliedthe “method of models”, of artificially reproducing series similar to those actually observedbut formed in accord with some plan and therefore possessing a definite origin.The five years from 1924 to 1928, in spite of all the troubles, anxieties and prolongedhousing inconveniences caused by his move to Moscow, became a most fruitful period inSlutsky’s life. During that time, he achieved three considerable aims: he developed the theoryof stochastic limit (and asymptote); discovered pseudo-periodic waves; and investigated theerrors of the coefficient of correlation between series consisting of terms connected with eachother.In 1928, E.E. participated at the Congress of Mathematicians in Bologna. The tripprovided great moral satisfaction and was a grand reward deserved by sleepless nights andcreative enthusiasm. His report on stochastic asymptotes and limits attracted everyone. Aconsiderable debate flared up at the Congress between E.E. and the eminent Italianmathematician Cantelli concerning the priority to the strong law of large numbers. Slutsky[16] had stated that it was due to Borel but Cantelli considered himself its author.Castelnuovo, the famous theoretician of probability, and other Italian mathematicians ralliedtogether with Cantelli against Slutsky, declared that Borel’s book, to which E.E. had referredto, lacked anything of the sort attributed to him by the Russian mathematician, and demandedan immediate explanation from him. E.E. had to repulse numerous attacks launched by theItalians and to prove his case.The point was that Slutsky, having been restricted by the narrow boundaries of a paperpublished in the C.r. Acad. Sci. Paris, had not expressed himself quite precisely. He indicatedthat Borel was the first to consider the problem and that Cantelli, Khinchin, Steinhaus and hehimself studied it later on. However, he should have singled out Cantelli and stressed his