# Itō Kiyoshi

**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 .

## Life

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.

## Awards

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

- Asahi Prize (1977),
- Israeli Wolf Prize (1987)
- Kyoto Prize (1998)
- Person of Special Cultural Merit (2003)
- Carl Friedrich Gauß Prize (2006), first prize winner
- Order of Culture (2008)

## Fonts

- 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)

## Web links

- Literature by and about Itō Kiyoshi in the catalog of the German National Library
- John J. O'Connor, Edmund F. Robertson :
*Itō Kiyoshi.*In:*MacTutor History of Mathematics archive .* - New York Times , "Kiyoshi Ito, 93, Mathematician Who Described Random Motion, Dies," Nov. 23, 2008
- Page on RIMS

personal data | |
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SURNAME | Itō, Kiyoshi |

ALTERNATIVE NAMES | Itô Kiyoshi; 伊藤 潔 (Japanese) |

BRIEF DESCRIPTION | Japanese mathematician |

DATE OF BIRTH | September 7, 1915 |

PLACE OF BIRTH | Hokusei -chō (now Inabe ), Japan |

DATE OF DEATH | November 10, 2008 |

Place of death | Kyoto |