Selected Papers

by Kiyoshi Itō, Daniel W. Stroock (Editor), S.R.S. Varadhan (Editor)

The central and distinguishing feature shared by all the contributions made by K. Ito is the extraordinary insight which they convey. Reading his papers, one should try to picture the intellectual setting in which he was working. At the time when he was a student in Tokyo during the late 1930s, probability theory had only recently entered the age of continuous-time stochastic processes: N. Wiener had accomplished his amazing construction little more than a decade earlier (Wiener, N., "Differential space," J. Math. Phys. 2, (1923)), Levy had hardly begun the mysterious web he was to eventually weave out of Wiener's P !hs, the generalizations started by Kolmogorov (Kol mogorov, A. N., "Uber die analytische Methoden in der Wahrscheinlichkeitsrechnung," Math Ann. 104 (1931)) and continued by Feller (Feller, W., "Zur Theorie der stochastischen Prozesse," Math Ann. 113, (1936)) appeared to have little if anything to do with probability theory, and the technical measure-theoretic tours de force of J. L. Doob (Doob, J. L., "Stochastic processes depending on a continuous parameter, " TAMS 42 (1937)) still appeared impregnable to all but the most erudite. Thus, even at the established mathematical centers in Russia, Western Europe, and America, the theory of stochastic processes was still in its infancy and the student who was asked to learn the subject had better be one who was ready to test his mettle.

647 pages, Paperback

First published December 16, 1986

About the author

Professor Kiyosi Itô is one of the most distinguished probability theorists in the world. He is the creator of a branch of mathematics that deals with stochastics and probabilities, now known as Itō calculus in his honour, and one of its main tools is the stochastic integral, also known as Itō integral. This calculus plays a fundamental role in modern financial mathematics.

Itō died in Kyoto, Japan, in 2008. He was 93 years old.