Itô’s Stochastic Calculus and Probability Theory

  • Nobuyuki Ikeda
  • Shinzo Watanabe
  • Masatoshi Fukushima
  • Hiroshi Kunita

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Masatoshi Fukushima, Matsuyo Tomisaki
    Pages 51-61
  3. Leonard Gross, Paul Malliavin
    Pages 73-116
  4. Keisuke Hara, Yoichiro Takahashi
    Pages 117-128
  5. Yasuji Hashimoto, Shojiro Manabe, Yukio Ogura
    Pages 129-139
  6. Nobuyuki Ikeda, Shojiro Manabe
    Pages 141-156
  7. Shigeo Kusuoka
    Pages 213-231
  8. Masao Nagasawa, Thomas Domenig
    Pages 261-280
  9. Tokuzo Shiga
    Pages 311-326
  10. Ichiro Shigekawa, Setsuo Taniguchi
    Pages 327-346
  11. Daniel W. Stroock
    Pages 355-371
  12. S. R. S. Varadhan
    Pages 385-400

About this book


Professor Kiyosi Ito is well known as the creator of the modern theory of stochastic analysis. Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater. For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future. For example, a basic formula, called the Ito formula, is well known and widely used in fields as diverse as physics and economics.
This volume contains 27 papers written by world-renowned probability theorists. Their subjects vary widely and they present new results and ideas in the fields where stochastic analysis plays an important role. Also included are several expository articles by well-known experts surveying recent developments. Not only mathematicians but also physicists, biologists, economists and researchers in other fields who are interested in the effectiveness of stochastic theory will find valuable suggestions for their research. In addition, students who are beginning their study and research in stochastic analysis and related fields will find instructive and useful guidance here.
This volume is dedicated to Professor Ito on the occasion of his eightieth birthday as a token of deep appreciation for his great achievements and contributions. An introduction to and commentary on the scientific works of Professor Ito are also included.


Applied Mathematics Probability theory Stochastic calculus calculus differential equation mathematics

Editors and affiliations

  • Nobuyuki Ikeda
    • 1
  • Shinzo Watanabe
    • 2
  • Masatoshi Fukushima
    • 3
  • Hiroshi Kunita
    • 4
  1. 1.Department of Computer ScienceRitsumeikan UniversityKusatsu, ShigaJapan
  2. 2.Department of Mathematics, Graduate School of ScienceKyoto UniversityKyotoJapan
  3. 3.Department of Mathematics, Faculty of Fundamental EngineeringOsaka UniversityToyonaka, Osaka, 560Japan
  4. 4.Graduate School of MathematicsKyushu UniversityFukuoka, 812Japan

Bibliographic information