Kiyoshi Itō at Cornell University, 1970
September 7, 1915|
Hokusei, Mie, Honshū, Japan
|Died||November 10, 2008
|Institutions||University of Kyoto|
|Alma mater||University of Tokyo|
|Doctoral advisor||Shokichi Iyanaga|
|Doctoral students||Masatoshi Fukushima
|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.
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.
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.
Itō died on November 10, 2008 in Kyoto, Japan at age 93.
- Itō's lemma
- Diffusion process
- Stochastic differential equation
- Itō diffusion
- Itō isometry
- Black–Scholes model
- "Renowned math wiz Ito, 93, dies", The Japan Times, November 15, 2008
- Lohr, Steve (November 23, 2008), "Kiyoshi 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 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.
- Obituary at The New York Times
- O'Connor, John J.; Robertson, Edmund F., "Kiyoshi Itō", MacTutor History of Mathematics archive, University of St Andrews.
- Protter, Philip (June–July 2007), "The Work of Kyoshi Itō" (.PDF), Notices of the American Mathematical Society 54 (6): 744–745, retrieved 2007-09-20
- Bibliography of Kiyoshi Itō
- Kiyoshi Itō at Research Institute for Mathematical Sciences
- Kiyoshi Itō at the Mathematics Genealogy Project