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Kiyosi Itô

January 07, 2023

Kiyosi Itô (伊藤 清, Itō Kiyoshi, Japanese pronunciation: [itoː kiꜜjoɕi], September 7, 1915 – 10 November 2008) was a Japanese mathematician who made fundamental contributions to probability theory, in particular, the theory of stochastic processes. He invented the concept of stochastic integral and stochastic differential equation, and is known as the founder of so-called Itô calculus.

Kiyosi Itô
Itô at Cornell University, 1970
Born(1915-09-07)September 7, 1915
Hokusei, Mie, Japan
DiedNovember 10, 2008(2008-11-10) (aged 93)[1]
Kyoto, Japan
Alma materUniversity of Tokyo
Known forItô calculus
AwardsAsahi Prize (1977)
Wolf Prize (1987)
Kyoto Prize (1998)
Gauss Prize (2006)
Scientific career
FieldsMathematics
InstitutionsUniversity of Kyoto
Doctoral advisorShokichi Iyanaga
Doctoral studentsShinzo Watanabe
InfluencesNorbert Wiener, Paul Lévy
InfluencedJean-Michel Bismut
Robert C. Merton[2]
Hans Föllmer
Daniel W. Stroock
S. R. Srinivasa Varadhan
Marc Yor

Overview

 
Itô (right) with Issei Shiraishi in 1935. Shiraishi later became a mathematician.

Itô pioneered the theory of stochastic integration and stochastic differential equations, now known as 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. Itô also made contributions to the study of diffusion processes on manifolds, known as stochastic differential geometry.[3]

Although the standard Hepburn romanization of his name is Kiyoshi Itō, he used the spelling Kiyosi Itô (Kunrei-shiki romanization). The alternative spellings Itoh and Ito are also sometimes seen in the West.

Biography

 
Kiyosi Itô (right) with Seizō Itō in 1937. Seizō is Kiyosi's brother. Seizō later became a mathematician.

Itô was born in Hokusei-cho[4] 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, including a series of articles in which he defined the stochastic integral and laid the foundations of the Itō calculus. 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 to which he remained affiliated 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, New Jersey, 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.[5]

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

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

Scientific works of Kiyosi Itô

 
Itô at the Cabinet Statistics Bureau in 1940
  • Kiyosi Itô (1940). "On the Probability Distribution on a Compact Group". Proceedings of the Physico-Mathematical Society of Japan. 3rd Series. 22 (12): 977–998.
  • Kiyosi Ito (1942). "Differential equations determining a Markoff process" (PDF). Zenkoku Sizyo Sugaku Danwakai-si (J. Pan-Japan Math. Coll.) (1077): 1352–1400.
  • Kiyosi Itô (1944). "Stochastic integral". Proceedings of the Imperial Academy. 20 (8): 519–524. doi:10.3792/pia/1195572786.
  • Kiyosi Itô (1946). "On a stochastic integral equation". Proceedings of the Japan Academy. 22 (2): 32–35. doi:10.3792/pja/1195572371.
  • Kiyosi Itô (1950). "Stochastic differential equations in a differentiable manifold". Nagoya Mathematical Journal. 1: 35–47. doi:10.1017/S0027763000022819.
  • Kiyosi Itô (1951). "On a formula concerning stochastic differentials". Nagoya Mathematical Journal. 3: 55–65. doi:10.1017/S0027763000012216.

Notes

  1. ^ "Renowned math wiz Ito, 93, dies", The Japan Times, November 15, 2008
  2. ^ Robert C. Merton (1997) Nobel Lecture, December 1997.
  3. ^ Lohr, Steve (November 23, 2008), "Kiyosi Ito, 93, Mathematician Who Described Random Motion, Dies", The New York Times
  4. ^ Kiyoshi Ito Japanese mathematician / Encyclopedia Britannica
  5. ^ "Donald Keene, 7 others win Order of Culture," Yomiuri Shimbun. October 29, 2008 (in Japanese)

References

See also

External links

January 07, 2023
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This article includes a list of general references but it lacks sufficient corresponding inline citations Please help to improve this article by introducing more precise citations March 2018 Learn how and when to remove this template message Kiyosi Ito 伊藤 清 Itō Kiyoshi Japanese pronunciation itoː kiꜜjoɕi September 7 1915 10 November 2008 was a Japanese mathematician who made fundamental contributions to probability theory in particular the theory of stochastic processes He invented the concept of stochastic integral and stochastic differential equation and is known as the founder of so called Ito calculus Kiyosi ItoIto at Cornell University 1970Born 1915 09 07 September 7 1915Hokusei Mie JapanDiedNovember 10 2008 2008 11 10 aged 93 1 Kyoto JapanAlma materUniversity of TokyoKnown forIto calculusAwardsAsahi Prize 1977 Wolf Prize 1987 Kyoto Prize 1998 Gauss Prize 2006 Scientific careerFieldsMathematicsInstitutionsUniversity of KyotoDoctoral advisorShokichi IyanagaDoctoral studentsShinzo WatanabeInfluencesNorbert Wiener Paul LevyInfluencedJean Michel BismutRobert C Merton 2 Hans FollmerDaniel W Stroock S R Srinivasa VaradhanMarc Yor Contents 1 Overview 2 Biography 3 Scientific works of Kiyosi Ito 4 Notes 5 References 6 See also 7 External linksOverview Edit Ito right with Issei Shiraishi in 1935 Shiraishi later became a mathematician Ito pioneered the theory of stochastic integration and stochastic differential equations now known as Ito calculus Its basic concept is the Ito integral and among the most important results is a change of variable formula known as Ito s lemma Ito 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 3 Although the standard Hepburn romanization of his name is Kiyoshi Itō he used the spelling Kiyosi Ito Kunrei shiki romanization The alternative spellings Itoh and Ito are also sometimes seen in the West Biography Edit Kiyosi Ito right with Seizō Itō in 1937 Seizō is Kiyosi s brother Seizō later became a mathematician Ito was born in Hokusei cho 4 in Mie Prefecture on the main island of Honshu He graduated with a B S 1938 and a Ph D 1945 in Mathematics from the University of Tokyo Between 1938 and 1945 Ito worked for the Japanese National Statistical Bureau where he published two of his seminal works on probability and stochastic processes including a series of articles in which he defined the stochastic integral and laid the foundations of the Itō calculus 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 to which he remained affiliated until his retirement in 1979 Starting in the 1950s Ito spent long periods of time outside Japan at Cornell Stanford the Institute for Advanced Study in Princeton New Jersey and Aarhus University in Denmark Ito 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 Ito 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 Ito at a special ceremony held in Kyoto In October 2008 Ito was honored with Japan s Order of Culture and an awards ceremony for the Order of Culture was held at the Imperial Palace 5 Ito wrote in Japanese Chinese German French and English He died on November 10 2008 in Kyoto Japan at age 93 Scientific works of Kiyosi Ito Edit Ito at the Cabinet Statistics Bureau in 1940 Kiyosi Ito 1940 On the Probability Distribution on a Compact Group Proceedings of the Physico Mathematical Society of Japan 3rd Series 22 12 977 998 Kiyosi Ito 1942 Differential equations determining a Markoff process PDF Zenkoku Sizyo Sugaku Danwakai si J Pan Japan Math Coll 1077 1352 1400 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 doi 10 1017 S0027763000022819 Kiyosi Ito 1951 On a formula concerning stochastic differentials Nagoya Mathematical Journal 3 55 65 doi 10 1017 S0027763000012216 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 Notes Edit Renowned math wiz Ito 93 dies The Japan Times November 15 2008 Robert C Merton 1997 Nobel Lecture December 1997 Lohr Steve November 23 2008 Kiyosi Ito 93 Mathematician Who Described Random Motion Dies The New York Times Kiyoshi Ito Japanese mathematician Encyclopedia Britannica Donald Keene 7 others win Order of Culture Yomiuri Shimbun October 29 2008 in Japanese References EditObituary at The New York Times O Connor John J Robertson Edmund F Kiyosi Ito MacTutor History of Mathematics archive University of St Andrews Foellmer Hans May 2006 On Kiyosi Ito s Work and its Impact PDF retrieved 2020 09 20 Protter Philip June July 2007 The Work of Kyoshi Ito PDF Notices of the American Mathematical Society 54 6 744 745 retrieved 2007 09 20 Kunita Hiroshi May 2010 Ito s stochastic calculus its surprising power for applications Stochastic Processes and Their Applications 120 5 7622 652 doi 10 1016 j spa 2010 01 013See also EditIto calculus Ito diffusion Ito integral Ito isometry Ito s lemma Black Scholes modelExternal links EditKiyosi Ito 1915 2008 Eightieth Birthday Lecture RIMS Kyoto University September 1995 Research Institute for Mathematical Sciences Kyoto University Kyoto Bibliography of Kiyosi Ito Kiyosi Ito at Research Institute for Mathematical Sciences Kiyosi Ito at the Mathematics Genealogy Project Kiyoshi Ito Japanese mathematician Encyclopedia Britannica Retrieved from https en wikipedia org w index php title Kiyosi Ito amp oldid 1128363370, wikipedia, wiki, book, books, library,

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