Carl-Gustav Esseen

Carl- Gustav Esseen ( born September 18, 1918 † 10 November 2001) was a Swedish mathematician. He specialized in probability theory.

Life

Carl- Gustav Esseen attended school in Linköping. From 1936 he studied at the University of Uppsala mathematics, astronomy, physics and chemistry, and then worked as a research assistant at the University of Uppsala. Inspired by the work of Harald Cramér and Arne Beurling, he examined the accuracy of the approximation to the normal distribution in the central limit theorem and certain in the case of independent and identically distributed summands the best accuracy. This result, which he found irrespective of the mathematician Andrew C. Berry, is now known as the set of Berry - Esseen.

1944 Carl- Gustav Esseen received his doctorate with a thesis on the Fourier analysis of distribution functions. In 1949 he was appointed Full Professor of Applied Mathematics at the Royal Institute of Technology in Stockholm. In 1962 he was a professor at the Institute of Mathematical Statistics and 1967, the first Professor of Mathematical Statistics at the University of Uppsala. In 1984 he became Professor Emeritus.

Scientific Work

Although Esseen in most of his works dealt with the central limit theorem and related topics, he also made important contributions in other areas. Some of his writings had influence on industrial applications, for example, his studies on the control theory in telecommunications. After his retirement, he worked on topics from number theory, in particular with factorisation algorithms, which are of importance for cryptology.

Esseen supervised several PhD students. His lectures and writings were distinguished by their methodical preparation. His colleagues appreciated his ability to find work in inaccuracies and to correct them.

Honors

Festschrift

• Allan Gut, Lars Holst ( ed.): Probability and mathematical statistics. Essays in honor of Carl- Gustav Esseen. Festschrift for the 65th birthday of Carl- Gustav Esseen. Academic Press, New York 1983.

Writings

• On the Liapounoff limit of error in the theory of probability. In: Arkiv för Mathematics, Astronomy och Fysik. Stockholm 1942.
• Determination of the maximum deviation from the Gaussian law. Almqvist & Wiksell, Stockholm, 1943.
• Fourier analysis of distribution functions. A mathematical study of the Laplace - Gaussian law. Dissertation. In: Acta mathematica. 77, 1944.
• On Mean central limit theorem. Elander, Gothenburg 1958.
• Bounds for the absolute third moment. In: Scandinavian Journal of Statistics. Volume 2 Blackwell, Oxford, 1975, ISSN 0303-6898, pp. 149-152.
• Svante Janson with: On moment conditions for normed sums of independent variables and martingale differences. Uppsala 1983.
• A stochastic model for primitive roots. Uppsala 1991.