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Carl-Gustav Esseen

January 07, 2023

Carl-Gustav Esseen (13 September 1918 in Linköping[1] – 10 November 2001) was a Swedish mathematician. His work was in the theory of probability. The Berry–Esseen theorem is named after him.[2]

Life

Carl-Gustav Esseen attended school in Linköping. Starting in 1936, he studied mathematics, astronomy, physics and chemistry at the University of Uppsala. Inspired by the harmonic-analytic research of Harald Cramér and Arne Beurling, Esseen examined the accuracy of the approximation to the normal distribution in the central limit theorem in the case of independent and identically distributed summands. Esseen's bound is now called "the Berry-Esseen theorem", because it was independently proved by Andrew C. Berry, also.[2]

In 1944 Esseen received his doctorate with a thesis on the Fourier analysis of probability distributions. In 1949 he was appointed full professor of applied mathematics at the Royal Institute of Technology in Stockholm. In 1962 his professorship moved to the field of mathematical statistics and in 1967, he became first holder of the chair of mathematical statistics at the University of Uppsala. He retired in 1984.[2][3]

Scientific work

Although Esseen worked mostly on the central limit theorem and related topics, he also worked in other areas. Some industrial applications were considered in his writings, for example, his studies on control theory and in telecommunications. After retirement, Esseen worked on topics from number theory, especially factorization, a topic of importance in cryptology.[2]

Esseen supervised several doctoral students. His lectures and writings were meticulously prepared and delivered.

Honours

Selected works

  • "On the Liapounoff limit of error in the theory of probability", Arkiv för Mathematik, Astronomi och Fysik 28A, #9 (1942), 19 pp., MR0011909.
  • "Determination of the maximum deviation from the Gaussian law", Arkiv för Mathematik, Astronomi och Fysik 29A, #20 (1943), 10 pp., MR0011910.
  • "Fourier analysis of distribution functions. A mathematical study of the Laplace–Gaussian law", Acta Mathematica 77, #1 (December 1945), pp. 1–125, MR0014626, doi:10.1007/BF02392223. (Dissertation)
  • "On mean central limit theorems", Kungl. Tekn. Högsk. Handl. Stockholm #121 (1958), 31 pp., MR0097111.
  • "Bounds for the absolute third moment", Scandinavian Journal of Statistics (ISSN 0303-6898) 2, #3 (1975), pp. 149–152, MR0383495, JSTOR 4615595.
  • (with Svante Janson) "On moment conditions for normed sums of independent variables and martingale differences", Stochastic Processes and their Applications 19, #1 (1985), pp. 173–182, MR0780729, doi:10.1016/0304-4149(85)90048-1.
  • "A stochastic model for primitive roots", Revue Roumaine de Mathématiques Pures et Appliquées 38, #6 (1993), pp. 481–501, MR1258051.

References

  1. ^ "Esseen, Carl-Gustaf H:son" in Who's Who 1969
  2. ^ a b c d e Carl-Gustav Esseen[permanent dead link], Bernoulli News, Newsletter of the Bernoulli Society for Mathematical Statistics and Probability 9, #1 (May 2002).
  3. ^ A brief history of the professors at the department of Mathematics 8 June 2011 at the Wayback Machine, department of mathematics, KTH Royal Institute of Technology. Accessed on line 28 April 2010.

External links

January 07, 2023
carl, gustav, esseen, september, 1918, linköping, november, 2001, swedish, mathematician, work, theory, probability, berry, esseen, theorem, named, after, life, edit, attended, school, linköping, starting, 1936, studied, mathematics, astronomy, physics, chemis. Carl Gustav Esseen 13 September 1918 in Linkoping 1 10 November 2001 was a Swedish mathematician His work was in the theory of probability The Berry Esseen theorem is named after him 2 Life EditCarl Gustav Esseen attended school in Linkoping Starting in 1936 he studied mathematics astronomy physics and chemistry at the University of Uppsala Inspired by the harmonic analytic research of Harald Cramer and Arne Beurling Esseen examined the accuracy of the approximation to the normal distribution in the central limit theorem in the case of independent and identically distributed summands Esseen s bound is now called the Berry Esseen theorem because it was independently proved by Andrew C Berry also 2 In 1944 Esseen received his doctorate with a thesis on the Fourier analysis of probability distributions In 1949 he was appointed full professor of applied mathematics at the Royal Institute of Technology in Stockholm In 1962 his professorship moved to the field of mathematical statistics and in 1967 he became first holder of the chair of mathematical statistics at the University of Uppsala He retired in 1984 2 3 Scientific work EditAlthough Esseen worked mostly on the central limit theorem and related topics he also worked in other areas Some industrial applications were considered in his writings for example his studies on control theory and in telecommunications After retirement Esseen worked on topics from number theory especially factorization a topic of importance in cryptology 2 Esseen supervised several doctoral students His lectures and writings were meticulously prepared and delivered Honours Edit1963 Elected Member of the Royal Swedish Academy of Engineering Sciences 2 Selected works Edit On the Liapounoff limit of error in the theory of probability Arkiv for Mathematik Astronomi och Fysik 28A 9 1942 19 pp MR0011909 Determination of the maximum deviation from the Gaussian law Arkiv for Mathematik Astronomi och Fysik 29A 20 1943 10 pp MR0011910 Fourier analysis of distribution functions A mathematical study of the Laplace Gaussian law Acta Mathematica 77 1 December 1945 pp 1 125 MR0014626 doi 10 1007 BF02392223 Dissertation On mean central limit theorems Kungl Tekn Hogsk Handl Stockholm 121 1958 31 pp MR0097111 Bounds for the absolute third moment Scandinavian Journal of Statistics ISSN 0303 6898 2 3 1975 pp 149 152 MR0383495 JSTOR 4615595 with Svante Janson On moment conditions for normed sums of independent variables and martingale differences Stochastic Processes and their Applications 19 1 1985 pp 173 182 MR0780729 doi 10 1016 0304 4149 85 90048 1 A stochastic model for primitive roots Revue Roumaine de Mathematiques Pures et Appliquees 38 6 1993 pp 481 501 MR1258051 References Edit Esseen Carl Gustaf H son in Who s Who 1969 a b c d e Carl Gustav Esseen permanent dead link Bernoulli News Newsletter of the Bernoulli Society for Mathematical Statistics and Probability 9 1 May 2002 A brief history of the professors at the department of Mathematics Archived 8 June 2011 at the Wayback Machine department of mathematics KTH Royal Institute of Technology Accessed on line 28 April 2010 External links EditCarl Gustav Esseen at the Mathematics Genealogy Project Retrieved from https en wikipedia org w index php title Carl Gustav Esseen amp oldid 1113895556, wikipedia, wiki, book, books, library,

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