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.