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Selected Works of A. N. Kolmogorov pp 442–458Cite as

Random Functions and Limit Theorems

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Part of the book series: Mathematics and Its Applications (Soviet Series) ((MASS,volume 26))

Abstract

Without claiming to present an exhaustive review of the literature on the question, we intend to give an outline of the first steps of the theory of random functions, possible basic methods for a systematic construction of this theory and basic problems concerning functional methods in limit theorems; in addition, we report certain comparatively new results.

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‘Zufällige Funktionen und Grenzverteilungssätze’, In: Bericht über die Tagung Wahrscheinlichkeitsrechnung und mathematische Statistik, Berlin, 1956, pp.113-126.

1

The papers presented by Kolmogorov and Prokhorov at the conference are dose to those of M. Fréchet and R. Fortet. In his talk given on the last day of the conference Kolmogorov presented new results obtained by Prokhorov in between his talk and that of A.N. Kolmogorov. Therefore the authors deemed it appropriate to publish the joint text of their two papers. §4 (without Theorems IV and V) and §6 represent Prokhorov’s contribution, while §§1-3, 5 and Theorems IV and V from §4 constituted Kolmogorov’s paper. Theorems IV and V from §4 were proved by Prokhorov between his talk and that of Kolmogorov.

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Authors
  1. Yu. V. Prokhorov
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A. N. Shiryayev

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© 1992 Springer Science+Business Media Dordrecht

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Prokhorov, Y.V. (1992). Random Functions and Limit Theorems. In: Shiryayev, A.N. (eds) Selected Works of A. N. Kolmogorov. Mathematics and Its Applications (Soviet Series), vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2260-3_44

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  • DOI: https://doi.org/10.1007/978-94-011-2260-3_44

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5003-6

  • Online ISBN: 978-94-011-2260-3

  • eBook Packages: Springer Book Archive

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