Kiyosi Itô

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Kiyosi Itô
Kiyoshi Ito cropped 3 Kiyosi Ito.jpg
Itô at Cornell University, 1970
Born(1915-09-07)September 7, 1915
DiedNovember 10, 2008(2008-11-10) (aged 93)[1]
Alma materUniversity of Tokyo
Known forItô calculus
AwardsAsahi Prize (1977)
Wolf Prize (1987)
Kyoto Prize (1998)
Gauss Prize (2006)
Scientific career
InstitutionsUniversity of Kyoto
Doctoral advisorShokichi Iyanaga
Doctoral studentsShinzo Watanabe
InfluencesNorbert Wiener, Paul Lévy
InfluencedJean-Michel Bismut
Robert C. Merton[2]
Hans Föllmer
Daniel W. Stroock
S. R. Srinivasa Varadhan
Marc Yor

Kiyosi Itô (伊藤 清, Itō Kiyoshi, Japanese pronunciation: [itoː kiꜜjoɕi], September 7, 1915 – 10 November 2008) was a Japanese mathematician who made fundamental contributions to probability theory, in particular, the theory of stochastic processes. He invented the concept of stochastic integral and stochastic differential equation, and is known as the founder of so-called Itô calculus.


Itô (right) with Issei Shiraishi in 1935. Shiraishi later became a mathematician.

Itô pioneered the theory of stochastic integration and stochastic differential equations, now known as Itô calculus. Its basic concept is the Itô integral, and among the most important results is a change of variable formula known as Itô's lemma. Itô calculus is a method used in the mathematical study of random events and is applied in various fields, and is perhaps best known for its use in mathematical finance. Itô also made contributions to the study of diffusion processes on manifolds, known as stochastic differential geometry.[3]

Although the standard Hepburn romanization of his name is Kiyoshi Itō, he used the spelling Kiyosi Itô (Kunrei-shiki romanization). The alternative spellings Itoh and Ito are also sometimes seen in the West.


Kiyosi Itô (right) with Seizō Itō in 1937. Seizō is Kiyosi's brother. Seizō later became a mathematician.

Itô was born in Hokusei-cho[4] in Mie Prefecture on the main island of Honshū. He graduated with a B.S. (1938) and a Ph.D (1945) in Mathematics from the University of Tokyo. Between 1938 and 1945, Itô worked for the Japanese National Statistical Bureau, where he published two of his seminal works on probability and stochastic processes, including a series of articles in which he defined the stochastic integral and laid the foundations of the Itō calculus. After that he continued to develop his ideas on stochastic analysis with many important papers on the topic.

In 1952, he became a Professor at the University of Kyoto to which he remained affiliated until his retirement in 1979. Starting in the 1950s, Itô spent long periods of time outside Japan, at Cornell, Stanford, the Institute for Advanced Study in Princeton, New Jersey, and Aarhus University in Denmark.

Itô was awarded the inaugural Gauss Prize in 2006 by the International Mathematical Union for his lifetime achievements. As he was unable to travel to Madrid, his youngest daughter, Junko Itô received the Gauss Prize from the King of Spain on his behalf. Later, International Mathematics Union (IMU) President Sir John Ball personally presented the medal to Itô at a special ceremony held in Kyoto.

In October 2008, Itô was honored with Japan's Order of Culture, and an awards ceremony for the Order of Culture was held at the Imperial Palace.[5]

Itô wrote in Japanese, Chinese, German, French and English.

He died on November 10, 2008 in Kyoto, Japan at age 93.

Scientific works of Kiyosi Itô[edit]

Itô at the Cabinet Statistics Bureau in 1940
  • Kiyosi Itô (1940). "On the Probability Distribution on a Compact Group". Proceedings of the Physico-Mathematical Society of Japan. 3rd Series. 22 (12): 977–998.



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