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  • © 1996

Itô’s Stochastic Calculus and Probability Theory

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  • ISBN: 978-4-431-68532-6
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Table of contents (27 chapters)

  1. Front Matter

    Pages i-xiv
  2. On decomposition of additive functionals of reflecting Brownian motions

    • Masatoshi Fukushima, Matsuyo Tomisaki
    Pages 51-61
  3. Hall’s transform and the Segal-Bargmann map

    • Leonard Gross, Paul Malliavin
    Pages 73-116
  4. Lagrangian for pinned diffusion process

    • Keisuke Hara, Yoichiro Takahashi
    Pages 117-128
  5. Short Time Asymptotics and an Approximation for the Heat Kernel of a Singular Diffusion

    • Yasuji Hashimoto, Shojiro Manabe, Yukio Ogura
    Pages 129-139
  6. Van Vleck-Pauli formula for Wiener integrals and Jacobi fields

    • Nobuyuki Ikeda, Shojiro Manabe
    Pages 141-156
  7. A Remark on American Securities

    • Shigeo Kusuoka
    Pages 213-231
  8. Diffusion processes on an open time interval and their time reversal

    • Masao Nagasawa, Thomas Domenig
    Pages 261-280

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.

Keywords

  • Applied Mathematics
  • Probability theory
  • Stochastic calculus
  • calculus
  • differential equation
  • mathematics

Editors and Affiliations

  • Department of Computer Science, Ritsumeikan University, Kusatsu, Shiga, Japan

    Nobuyuki Ikeda

  • Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, Japan

    Shinzo Watanabe

  • Department of Mathematics, Faculty of Fundamental Engineering, Osaka University, Toyonaka, Osaka, 560, Japan

    Masatoshi Fukushima

  • Graduate School of Mathematics, Kyushu University, Fukuoka, 812, Japan

    Hiroshi Kunita

Bibliographic Information

  • Book Title: Itô’s Stochastic Calculus and Probability Theory

  • Editors: Nobuyuki Ikeda, Shinzo Watanabe, Masatoshi Fukushima, Hiroshi Kunita

  • DOI: https://doi.org/10.1007/978-4-431-68532-6

  • Publisher: Springer Tokyo

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Tokyo 1996

  • Softcover ISBN: 978-4-431-68534-0

  • eBook ISBN: 978-4-431-68532-6

  • Edition Number: 1

  • Number of Pages: XIV, 422

  • Topics: Probability Theory, Mathematics

Buying options

eBook
USD 74.99
Price excludes VAT (USA)
  • ISBN: 978-4-431-68532-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 99.00
Price excludes VAT (USA)