Itō Kiyoshi

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Itō Kiyoshi at Cornell University , 1970

Itō Kiyoshi ( Japanese 伊藤 清 ; born September 7, 1915 in Hokusei -chō (today Inabe ), Mie Prefecture ; † November 10, 2008 in Kyoto ) was a Japanese mathematician .


He examined stochastic processes and laid the foundation for the theory of stochastic integration and stochastic differential equations in two papers published in 1944 and 1946 . That is why Itō is now considered the founder of stochastic analysis .

Itō comes from a farming village west of Nagoya and after graduating from school began studying mathematics at the Imperial University of Tokyo , which he graduated at the age of 23. During his studies he had already felt drawn to the probability theory , which was not yet too developed at the time, which Paul Lévy and Andrei Kolmogorow were working on at the time . He then took up a position in the Japanese National Statistics Office , where he developed most of his theories during the war years. 1940 and 1942 he put - without first doctorate to have - his ideas in the two works about probability distributions on compact groups and over stochastic processes and infinitely divisible distributions represent these two essays that today are classified revolutionary than, found that time -. Also as a result of Japanese isolation during and after the Pacific War - little recognition.

It was not until 1945 that he was awarded the doctorate for his achievements , and in 1952 he was appointed full professor at the University of Kyoto . In addition to guest stays at the Institute for Advanced Study in Princeton , Bombay , at the University of Aarhus and Cornell University , he worked there until his retirement in 1979.

Itō's ideas, especially his Ito calculus of stochastic integration , have found application in many areas of the natural and economic sciences , for example in financial mathematics (there first in the famous Black-Scholes model for option pricing). The Itō process (also called the generalized Wiener process ), the Itō lemma and the Itō isometry are named after Itō . In mathematical literature, Itô is usually written instead of Itō.

Itō also received honorary doctorates from several universities around the world, such as the ETH Zurich . In 1998 he was elected to the National Academy of Sciences . He had been married since 1939 and had three daughters. In addition to English, French and Chinese, he also spoke (or rather, wrote) German.


Itō's life's work has been honored with many internationally renowned prizes:


  • with Y. Kawada: On the probability distribution on a compact group , Proc. Phys.-Math. Soc. Japan, Vol. 22, 1940, pp. 977-998
  • On stochastic processes, I (Infinitely divisible laws of probability), Japan J. Math., Vol. 18, 1942, pp. 261-301.
  • with Henry McKean : Diffusion processes and their sample paths, Springer, Grundlehren der Mathematischen Wissenschaften, 1965, 1974
  • Selected papers, Springer 1987 (editors SRSVaradhan, Daniel Stroock)
  • Stochastic processes, Lectures given at Aarhus University, editors Ole E. Barndorff-Nielsen, Ken-iti Sato, Springer-Verlag, 2004 (first 1969).
  • Lectures on stochastic processes, Springer 1984 (Lectures Tata Institute, Bombay)

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