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| footnotes = }} 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 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. 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 lengthy stints 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 on, 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.〔( "Donald Keene, 7 others win Order of Culture," ) ''Yomiuri Shimbun.'' October 29, 2008 (in Japanese)〕 Itô wrote in Japanese, Chinese, German, French and English. Itô died on November 10, 2008 in Kyoto, Japan at age 93. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kiyosi Itô」の詳細全文を読む スポンサード リンク
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