Brownian Motion

  • T. Hida

Part of the Applications of Mathematics book series (SMAP, volume 11)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. T. Hida
    Pages 1-43
  3. T. Hida
    Pages 44-113
  4. T. Hida
    Pages 132-184
  5. T. Hida
    Pages 185-231
  6. T. Hida
    Pages 232-251
  7. Back Matter
    Pages 293-327

About this book

Introduction

Following the publication of the Japanese edition of this book, several inter­ esting developments took place in the area. The author wanted to describe some of these, as well as to offer suggestions concerning future problems which he hoped would stimulate readers working in this field. For these reasons, Chapter 8 was added. Apart from the additional chapter and a few minor changes made by the author, this translation closely follows the text of the original Japanese edition. We would like to thank Professor J. L. Doob for his helpful comments on the English edition. T. Hida T. P. Speed v Preface The physical phenomenon described by Robert Brown was the complex and erratic motion of grains of pollen suspended in a liquid. In the many years which have passed since this description, Brownian motion has become an object of study in pure as well as applied mathematics. Even now many of its important properties are being discovered, and doubtless new and useful aspects remain to be discovered. We are getting a more and more intimate understanding of Brownian motion.

Keywords

Brownian motion Brownsche Bewegung Gaussian distribution Martingale Probability distribution Probability space Random variable Stochastic processes Variance random measure stochastic process

Authors and affiliations

  • T. Hida
    • 1
  1. 1.Department of Mathematics Faculty of ScienceNagoya UniversityChikasu-Ku, Nagoya 464Japan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-6030-1
  • Copyright Information Springer-Verlag New York 1980
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6032-5
  • Online ISBN 978-1-4612-6030-1
  • Series Print ISSN 0172-4568
  • About this book