Selected Papers - Tapa dura

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.

Kiyosi Ito (1915 - 2008) was one of the pioneers of probability theory, and the originator of Ito Calculus. First published in 1942 in Japanese, this epoch-making theory of stochastic differential equations describes nondeterministic and random evolutions. The Ito formula has found applications in other branches of mathematics as well as in various other fields including e.g., conformal field theory in physics, stochastic control theory in engineering, population genetics in biology and mathematical finance in economics. Besides being renowned for his brilliant mathematical achievements during a long and productive career spanning over sixty years, Ito has been a truly inspirational teacher to many mathematicians. He has received numerous awards and honors, including the 1987 Wolf Foundation Prize in Mathematics, the 1998 Kyoto Prize in Basic Sciences and the 2003 Japanese Cultural Merit Prize. In 2006, Ito was awarded the first Carl Friedrich Gauss Prize for Applications of Mathematics. This book contains a selection of 38 papers published between 1941 and 1983.