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Carl-Gustav Esseen (born September 18, 1918; died November 10, 2001) was a Swedish mathematician. His work was in the theory of probability.[1]
Life
Carl-Gustav Esseen attended school in Linköping. Starting in 1936, he studied mathematics, astronomy, physics and chemistry at the University of Uppsala, 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 in the case of independent and identically distributed summands. This result, also found independently by Andrew C. Berry, is now known as the Berry-Esseen theorem.[1]
In 1944 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 Professor at the Institute of Mathematical Statistics and in 1967, the first Professor of Mathematical Statistics at the University of Uppsala. In 1984 he retired and became professor emeritus.[1]
Scientific work
Although Esseen worked mostly on the Central Limit Theorem and related topics, he made important contributions in other areas. Some of his writings had impact on industrial applications, for example, his studies on control theory in telecommunications. After retirement, he worked on topics from number theory, especially factorization, which is of importance for cryptology.[1]
Esseen supervised several doctoral students. His lectures and writings were distinguished by their methodical preparation. His colleagues appreciated his ability to find work and to correct inaccuracies.
Honours
- 1963: Elected Member of the Royal Swedish Academy of Engineering Sciences.[1]
Selected works
- "On the Liapounoff Limit of error in the theory of probability." In: Arkiv för Mathematik, Astronomi 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, #1 (December, 1945), pp. 1–125, doi:10.1007/BF02392223.
- "On Mean Central Limit Theorems." Elander, Göteborg 1958.
- "Bounds for the absolute third moment." In: Scandinavian Journal of Statistics. Band 2. Blackwell, Oxford 1975, ISSN 0303-6898, pp. 149–152.
- (with Svante Janson) "On moment conditions for normed sums of independent variables and Martingale differences" Uppsala 1983.
- "A stochastic model for primitive roots." Uppsala 1991.