Kiyoshi Itō

Kiyoshi Itō
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.

Biography

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.

See also

• Itō's lemma
• Diffusion process
• Stochastic differential equation
• Itō diffusion
• Itō isometry
• Black–Scholes model

Notes

Scientific works of Kiyoshi Itō

• Kiyosi Ito (1944). "Stochastic integral". Proceedings of the Imperial Academy 20 (8): 519–524. doi:10.3792/pia/1195572786. 

• Kiyosi Ito (1946). "On a stochastic integral equation.". Proceedings of the Japan Academy 22 (2): 32–35. doi:10.3792/pja/1195572371. 

• Kiyosi Ito (1950). "Stochastic differential equations in a differentiable manifold". Nagoya Mathematical Journal 1: 35–47. 

• Kiyosi Ito (1951). "On a formula concerning stochastic differentials". Nagoya Mathematical Journal 3: 55–65. 

• Kiyosi Ito and Henry McKean (1974). Diffusion Processes and Their Sample Paths. Berlin: Springer Verlag. ISBN 978-3-540-60629-1. 

• Kiyosi Ito (1984). Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 978-0-89871-193-6. 

References

External links

• Bibliography of Kiyoshi Itō
• Kiyoshi Itō at Research Institute for Mathematical Sciences
• Kiyoshi Itō at the Mathematics Genealogy Project