# Kiyosi Itô

Kiyosi Itô | |
---|---|

Kiyosi Itô at Cornell University, 1970 | |

Born |
Hokusei, Mie, Honshū, Japan | September 7, 1915

Died |
November 10, 2008 93)^{[1]}Kyōto, Japan | (aged

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 (Kunrei-shiki romanization). The alternative spellings Itoh and Ito are also sometimes seen in the West.

## 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 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

- 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 2007-09-20

## External links

- Bibliography of Kiyosi Itô
- Kiyosi Itô at Research Institute for Mathematical Sciences
- Kiyosi Itô at the Mathematics Genealogy Project