Kiyoshi Itō

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Kiyoshi Itō
Kiyosi Ito.jpg
Kiyoshi Itō at Cornell University, 1970
Born (1915-09-07)September 7, 1915
Hokusei, Mie, Honshū, Japan
Died November 10, 2008(2008-11-10) (aged 93)[1]
Kyōto, Japan
Fields Mathematics
Institutions University of Kyoto
Alma mater University of Tokyo
Doctoral advisor Shokichi Iyanaga
Doctoral students Masatoshi Fukushima
Takeyuki Hida
Shigeo Kusuoka
Makiko Nisio
Murali Rao
Shinzo Watanabe
Toshio Yamada
Known for Itō calculus
Influences Norbert Wiener, Paul Lévy
Notable awards Asahi Prize (1977)
Wolf Prize in Mathematics (1987)
Kyoto Prize (1998)
Gauss Prize (2006)

Kiyoshi Itō (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 the Itō calculus. Its basic concept is the Itō integral, and among the most important results is a change of variable formula known as Itō's lemma. Itō calculus is a key tool in the mathematical study of random events and is widely applied in various fields, and is perhaps best known for its use in mathematical finance. Ito also made important contribution to the study of diffusion processes on manifolds, known as stochastic differential geometry.[2]

Although the standard Hepburn romanization of his name is Itō, the spellings Itô (Kunrei-shiki romanization), Itoh, or Ito are often seen in the West as well.


Itō 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, Itō 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.

In 1952, he became a Professor at the University of Kyoto where he remained until his retirement in 1979.

Starting in the 1950s, Itō spent lengthy stints outside Japan at Cornell, Stanford, the Institute for Advanced Study in Princeton, N.J. and Aarhus University in Denmark.

Itō 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 Itō received the Gauss Prize from the King of Spain on his behalf. Later on, International Mathematics Union (IMU) President Sir John Ball personally presented the medal to Itō at a special ceremony held in Kyoto.

In October 2008, Itō was honored with Japan's Order of Culture; and an awards ceremony for the Order of Culture was held at the Imperial Palace.[3]

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

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

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Scientific works of Kiyoshi Itō[edit]


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