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Diffusion Processes and their Sample Paths

  • Book
  • © 1996

Overview

Authors:
  1. Kiyosi Itô

    1. RIMS, Kyoto University, Sakyo-Ku, Kyoto, Japan
      Cornell University, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Henry P. McKean

    1. Courant Institute of Mathematical Sciences, New York University, New York, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Classics in Mathematics (CLASSICS)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XV
    Download chapter PDF

  2. Prerequisites

    • Kiyosi Itô, Henry P. McKean Jr.
    Pages 1-4

  3. The standard Brownian motion

    • Kiyosi Itô, Henry P. McKean Jr.
    Pages 5-40

  4. Brownian Local Times

    • Kiyosi Itô, Henry P. McKean Jr.
    Pages 40-83

  5. The general 1-dimensional diffusion

    • Kiyosi Itô, Henry P. McKean Jr.
    Pages 83-105

  6. Generators

    • Kiyosi Itô, Henry P. McKean Jr.
    Pages 105-164

  7. Time changes and killing

    • Kiyosi Itô, Henry P. McKean Jr.
    Pages 164-211

  8. Local and inverse local times

    • Kiyosi Itô, Henry P. McKean Jr.
    Pages 212-231

  9. Brownian motion in several dimensions

    • Kiyosi Itô, Henry P. McKean Jr.
    Pages 232-291

  10. A general view of diffusion in several dimensions

    • Kiyosi Itô, Henry P. McKean Jr.
    Pages 291-305

  11. Back Matter

    Pages 306-321
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Keywords

About this book

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.

Reviews

"The systematic character of the exposision, which makes from the widely ramified subject matter of the extensive literature a clear, masterly arranged whole, is a particularly valuable feature of this monograph." (Publicationes Mathematicae)

Authors and Affiliations

  • RIMS, Kyoto University, Sakyo-Ku, Kyoto, Japan

    Kiyosi Itô

  • Cornell University, USA

    Kiyosi Itô

  • Courant Institute of Mathematical Sciences, New York University, New York, USA

    Henry P. McKean

About the authors

Biography of Kiyosi Itô

Kiyosi Itô was born on September 7, 1915, in Kuwana, Japan. After his undergraduate and doctoral studies at Tokyo University, he was associate professor at Nagoya University before joining the faculty of Kyoto University in 1952. He has remained there ever since and is now Professor Emeritus, but has also spent several years at each of Stanford, Aarhus and Cornell Universities and the University of Minnesota.

Itô's fundamental contributions to probability theory, especially the creation of stochastic differential and integral calculus and of excursion theory, form a cornerstone of this field. They have led to a profound understanding of the infinitesimal development of Markovian sample paths, and also of applied problems and phenomena associated with the planning, control and optimization of engineering and other random systems.
Professor Itô has been the inspirer and teacher of an entire generation of Japanese probabilists.

Biography of Henry McKean

Henry McKean was born on December 14, 1930, in Wenham, Massachusetts. He studied mathematics at Dartmouth College, Cambridge University, and Princeton University; he received his degree from the last in 1955. He has held professional positions at Kyoto University, MIT, Rockefeller University, Weizmann Institute, Balliol College, Oxford, and the Courant Institute of Mathematical Sciences (1969 to present).  His main interests are probability, Hamiltonian mechanics, complex function theory, and nonlinear partial differential equations.

Bibliographic Information

  • Book Title: Diffusion Processes and their Sample Paths

  • Authors: Kiyosi Itô, Henry P. McKean

  • Series Title: Classics in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-62025-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1996

  • Softcover ISBN: 978-3-540-60629-1Published: 05 January 1996

  • eBook ISBN: 978-3-642-62025-6Published: 06 December 2012

  • Series ISSN: 1431-0821

  • Series E-ISSN: 2512-5257

  • Edition Number: 1

  • Number of Pages: XV, 323

  • Additional Information: Reprint of the 1974 Edition (Grundlehren der mathematischen Wissenschaften, Vol. 125)

  • Topics: Probability Theory and Stochastic Processes

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