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Selected Papers
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 ...
Stochastic Analysis and Related Topics in Kyoto
A collection of research and survey papers written by invited lecturers at the RIMS international symposium on stochastic analysis and related topics in celebration of Professor Kiyosi Itt's eighty-eighth birthday. It also covers topics such as quadratic Wiener functionals, representation of martingales, and Itt's construction procedure.
Stochastic Processes
This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with independent increments (the Lévy-Itô decomposition). It also contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. In addition, 70 exercises and their complete solutions are included.
Markov Processes from K. Itô's Perspective
Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that desc...
Essentials of Stochastic Processes
This book is an English translation of Kiyosi Ito's monograph published in Japanese in 1957. It gives a unified and comprehensive account of additive processes (or Levy processes), stationary processes, and Markov processes, which constitute the three most important classes of stochastic processes. Written by one of the leading experts in the field, this volume presents to the reader lucid explanations of the fundamental concepts and basic results in each of these three major areasof the theory of stochastic processes. With the requirements limited to an introductory graduate course on analysis (especially measure theory) and basic probability theory, this book is an excellent text for any g...
Shiké
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Diffusion Processes and their Sample Paths
Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.
East Asian Science
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A Diary of Darkness
A Diary of Darkness is one of the most important and compelling documents of wartime Japan. Between 1942 and 1945, the liberal journalist Kiyosawa Kiyoshi (1890-1945) kept at great personal risk a diary of his often subversive social and political observations and his personal struggles. The diary caused a sensation when it was published in Japan in 1948 and is today regarded as a classic. This is the first time it has appeared in English. Kiyosawa was an American-educated commentator on politics and foreign affairs who became increasingly isolated in Japan as militant nationalists rose to power. He began the diary as notes for a history of the war, but it soon became an "inadvertent autobio...
