Kiyosi Itô

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 (also known as the Itô formula). Itô also made contributions to the study of diffusion processes on manifolds, known as stochastic differential geometry. 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. In particular, the Itô's lemma's best known application is in the derivation of the Black–Scholes equation for option values. Fellow mathematician Daniel W. Stroock noted that "People all over realized that what Ito had done explained things that were unexplainable before." Economist Robert C. Merton stated that Itô's work had provided him "a very useful tool" in his own prize-winning work. 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 Western world. Itô was married with three daughters. ==Biography==

Itô was born on 7 September 1915 in a farming area located west of Nagoya, Japan, He excelled in his studies as a youth. After this period 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. This was his longest stint outside Japan. Among the courses he taught at Cornell was one in Higher Calculus. Itô wrote not only in Japanese but also in Chinese, German, French and English. When Itô left Cornell and returned to the University of Kyoto, he served as director of their Research Institute for Mathematical Sciences. Later, IMU President Sir John Macleod 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. Itô died on November 10, 2008, in Kyoto, Japan, at age 93, of respiratory failure. ==Selected publications==

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