Kiyoshi Itô
Native spelling: 伊藤清
1915–2008, Hokusei (now Inabe), Mie Prefecture, Japan, Kyoto, Japan
Japanese probabilist who created stochastic integration and stochastic differential equations (Itô calculus and Itô's formula), providing the calculus of Brownian motion used throughout probability, physics, and mathematical finance.
Kiyoshi Itô studied mathematics at the Imperial University of Tokyo, graduating in 1938. Drawn to the new measure-theoretic probability of Andrey Kolmogorov and the intuitive sample-path ideas of Paul Lévy, he worked from 1939 to 1943 at the Cabinet Statistics Bureau in Tokyo, where a sympathetic director allowed him time to pursue research on his own during the Second World War.
In a 1942 paper, 'On Stochastic Processes (Infinitely Divisible Laws of Probability)', and a 1944 note, 'Stochastic Integral', Itô constructed an integral with respect to Brownian motion — whose paths are nowhere differentiable and of unbounded variation, so classical Stieltjes integration fails — and proved the chain rule now called Itô's formula (or Itô's lemma), with its characteristic second-order correction term. This gave a rigorous pathwise meaning to stochastic differential equations.
Itô received his doctorate in 1945, moved to Nagoya University and, in 1952, to a professorship at Kyoto University, where he later directed the Research Institute for Mathematical Sciences (1976–1979) while also holding positions at the Institute for Advanced Study, Aarhus, and Cornell. His calculus became the standard language of diffusion theory, stochastic control, and option pricing in mathematical finance, and he was honoured with the Wolf Prize (1987), the Kyoto Prize (1998), and the inaugural Carl Friedrich Gauss Prize (2006).
Workplaces: Nagoya University, Kyoto University, Cornell University
Japan