**Kiyosi Ito** was a Japanese mathematician who pioneered the theory of stochastic integration and stochastic differential equations. He won the Gauss prize in 2006.

- In 1938 Ito graduated from the University of Tokyo and in the following year he was appointed to the Cabinet Statistics Bureau.
- In 1940 he published On the probability distribution on a compact group on which he collaborated with Yukiyosi Kawada.
- In 1942, Dr. Ito began to reconstruct from scratch the concept of stochastic integrals, and its associated theory of analysis.
- Ito, who still did not have a doctorate at this time, would have to wait several years before the importance of his ideas would be fully appreciated and mathematicians would begin to contribute to developing the theory.
- In 1943 Ito was appointed as Assistant Professor in the Faculty of Science of Nagoya Imperial University.
- Volume 20 of the Proceedings of the Imperial Academy of Tokyo contains six papers by Ito: (1) On the ergodicity of a certain stationary process; (2) A kinematic theory of turbulence; (3) On the normal stationary process with no hysteresis; (4) A screw line in Hilbert space and its application to the probability theory; (5) Stochastic integral; and (6) On Student's test.
- In 1945 Ito was awarded his doctorate.
- In 1952 Ito was appointed to a Professorship at Kyoto University.
- In this book, Ito develops the theory on a probability space using terms and tools from measure theory.
- The years 1954-56 Ito spent at the Institute for Advanced Study at Princeton University.
- An important publication by Ito in 1957 was Stochastic processes.
- In 1960 Ito visited the Tata Institute in Bombay, India, where he gave a series of lectures surveying his own work and that of other on Markov processes, Levy processes, Brownian motion and linear diffusion.
- Although Ito remained as a professor at Kyoto University until he retired in 1979, he also held positions as professor at Aarhus University from 1966 to 1969 and professor at Cornell University from 1969 to 1975.
- During his last three years at Kyoto before he retired, Ito was Director of the Research Institute for Mathematical Sciences there.
- Stochastic differential equations, called "Ito Formula," are currently in wide use for describing phenomena of random fluctuations over time.
- Calculation using the "Ito calculus" is common not only to scientists in physics, population genetics, stochastic control theory, and other natural sciences, but also to mathematical finance in economics.
- This ceaseless development has been led by many, including Dr. Ito, whose work in this regard is remarkable for its mathematical depth and strong interaction with a wide range of areas.
- Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater.
- For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future.
- For example, a basic formula, called the Ito formula, is well known and widely used in fields as diverse as physics and economics.

Born 7 September 1915, Hokusei-cho (now Inabe, Mie Prefecture), Japan. Died 10 November 2008, Kyoto, Japan.

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Origin Japan, Prize Wolf

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive