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Kiyosi Itô |
Kiyosi Itô passed away on November 10, 2008, in Kyoto, due to respiratory problems. A few days before, he had been awarded the “Order of Culture”, the highest distinction delivered by the Emperor of Japan. A formal reception had been held, for this occasion, in the Research Institute of Mathematical Sciences of Kyoto.
K. Itô was born in 1915, in the prefecture of Mie in Japan. His invention of stochastic calculus is by now a central element in Probability Theory. It took nearly twenty five years for this work, which had been elaborated between 1942 and 1950, to permeate the field until it became a standard topic taught in every course on advanced probability.
In 1970, K. Itô published a second revolutionary paper, in which he developed the theory of excursions of a Markov process. This work immediately inspired new studies, for Brownian excursions in particular, allowing to revisit and extend the pioneering work of Paul Lévy on this topic.
K. Itô is the co-author, with H.P. Mc Kean, of the book Diffusion Processes and their Sample paths (1965), which has been extremely influential in the study of diffusion processes, say between 1965 and 1980.
One should also mention Itô's book on infinite-dimensional Markov processes, a topic of which he was particularly fond, as can be seen from the Foreword in Selected Papers (1987) in which he writes: After several years it became my habit to observe even finite-dimensional facts from the infinite-dimensional viewpoint. Indeed, this viewpoint is extremely fruitful, as Itô's theory of excursions shows very clearly. I consider that Malliavin Calculus hinges upon the same general principle (this is not a very original statement!)
K. Itô has founded an extremely powerful probabilistic school in Japan; among his students let me mention N. Ikeda, H. Kunita, M. Fukushima and S. Watanabe, each of whom had also many students who continued to develop their master's field.
To summarize, K. Itô is one of the greatest probabilists of the twentieth century, in the same vein as P. Lévy and A. Kolmogorov.
Marc Yor
