Kiyosi Itô
Kiyosi Itô  

Kiyosi Itô at Cornell University, 1970


Born  Hokusei, Mie, Honshū, Japan 
September 7, 1915
Died  November 10, 2008 Kyōto, Japan 
(aged 93)^{[1]}
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  Itô calculus 
Influences  Norbert Wiener, Paul Lévy 
Notable awards  Asahi Prize (1977) Wolf Prize in Mathematics (1987) Kyoto Prize (1998) Gauss Prize (2006) 
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 the 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. Ito also made contributions to the study of diffusion processes on manifolds, known as stochastic differential geometry.^{[2]}
Although the standard Hepburn romanization of his name is Itō, he used the spelling Itô (Kunreishiki romanization). The alternative spellings Itoh and Ito are also sometimes seen in the West.
Contents
Biography
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.
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 also
 Itô's lemma
 Diffusion process
 Stochastic differential equation
 Itô diffusion
 Itô isometry
 Black–Scholes model
Notes
 ↑ "Renowned math wiz Ito, 93, dies", The Japan Times, November 15, 2008
 ↑ Lohr, Steve (November 23, 2008), "Kiyosi Ito, 93, Mathematician Who Described Random Motion, Dies", The New York Times
 ↑ "Donald Keene, 7 others win Order of Culture," Yomiuri Shimbun. October 29, 2008 (in Japanese)
Scientific works of Kiyosi Itô
 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 9783540606291.
 Kiyosi Ito (1984). Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 9780898711936.
References
 Obituary at The New York Times
 O'Connor, John J.; Robertson, Edmund F., "Kiyosi Itô", MacTutor History of Mathematics archive, University of St Andrews.
 Protter, Philip (June–July 2007), "The Work of Kyoshi Itô" (.PDF), Notices of the American Mathematical Society, 54 (6): 744–745, retrieved 20070920
External links
 Articles containing Japaneselanguage text
 1915 births
 2008 deaths
 People from Mie Prefecture
 20thcentury Japanese mathematicians
 21stcentury Japanese mathematicians
 Members of the United States National Academy of Sciences
 Probability theorists
 Wolf Prize in Mathematics laureates
 University of Tokyo alumni
 Kyoto University faculty
 Cornell University faculty
 Members of the French Academy of Sciences
 Researchers in stochastics
 Recipients of the Order of Culture
 Laureates of the Imperial Prize