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Kiyosi Itô (伊藤 清, Itō Kiyoshi, September 7, 1915 – 10 November 2008) was a Japanese mathematician. He 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.[2]

Kiyosi Itô
Kiyosi Ito.jpg
Kiyosi Itô at Cornell University, 1970
Born(1915-09-07)September 7, 1915
DiedNovember 10, 2008(2008-11-10) (aged 93)[1]
Kyoto, Japan
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
Toshio Yamada
InfluencesNorbert Wiener, Paul Lévy

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.


Itô was born in Hokusei 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. After that he continued to develop his ideas on stochastic analysis with many important papers on the topic. The stochastic calculus developed by Itô is one of the greatest tools ever developed in an applied sense, and is used not only in sciences and finance but also in biological systems, strategic decision making and computational sciences.

In 1952, he became a Professor at the University of Kyoto where he remained 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, N.J. 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.[3]

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

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

See alsoEdit


  1. ^ "Renowned math wiz Ito, 93, dies", The Japan Times, November 15, 2008
  2. ^ Lohr, Steve (November 23, 2008), "Kiyosi Ito, 93, Mathematician Who Described Random Motion, Dies", The New York Times
  3. ^ "Donald Keene, 7 others win Order of Culture," Yomiuri Shimbun. October 29, 2008 (in Japanese)

Scientific works of Kiyosi ItôEdit


External linksEdit