Home Business & Economics Brownian Motion
book: Brownian Motion
Book
Licensed
Unlicensed Requires Authentication

Brownian Motion

An Introduction to Stochastic Processes
  • René L. Schilling and Lothar Partzsch
  • With contributions by: Björn Böttcher
Language: English
Published/Copyright: 2014
Download eBook (PDF) Download eBook (EPUB)
Become an author with De Gruyter Brill
Explore this Subject How to publish with us
De Gruyter Textbook
This book is in the series
De Gruyter Textbook

About this book

Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance.

Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors’ aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs.

This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.

TEXT TEXT

Author / Editor information

René L. Schilling and Lothar Partzsch, Dresden University of Technology, Germany.

Supplementary Materials

Topics

  • Publicly Available

    Frontmatter

    I
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    Also of Interest

    II
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    Preface to the second edition

    V
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    Preface

    VI
    Download PDF
  • Publicly Available

    Contents

    IX
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    Dependence chart

    XIII
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    Index of notation

    XV
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    1. Robert Brown’s new thing

    1
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    2. Brownian motion as a Gaussian process

    7
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    3. Constructions of Brownian motion

    20
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    4. The canonical model

    38
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    5. Brownian motion as a martingale

    46
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    6. Brownian motion as a Markov process

    59
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    7. Brownian motion and transition semigroups

    81
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    8. The PDE connection

    114
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    9. The variation of Brownian paths

    136
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    10. Regularity of Brownian paths

    150
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    11. Brownian motion as a random fractal

    160
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    12. The growth of Brownian paths

    181
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    13. Strassen’s functional law of the iterated logarithm

    191
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    14. Skorokhod representation

    211
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    15. Stochastic integrals: L2-Theory

    220
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    16. Stochastic integrals: beyond L2T

    242
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    17 Itô’s formula

    248
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    18. Applications of Itô’s formula

    268
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    19. Stochastic differential equations

    290
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    20. Stratonovich’s stochastic calculus

    322
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    21. On diffusions

    332
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    22. Simulation of Brownian motion by Björn Böttcher

    345
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    A. Appendix

    359
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    Bibliography

    393
    Download PDF
  • Requires Authentication Unlicensed
    Licensed

    Index

    403
    Download PDF

Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 18, 2014
eBook ISBN:
9783110307306
Edition:
2nd revised and extended edition
Pages and Images/Illustrations in book
Front matter:
16
Main content:
408
https://doi.org/10.1515/9783110307306
eBook ISBN: 9783110307306
Keywords for this book
Markov process; Transition semigroups; Brownian paths; Strassen’s functional law of the iterated logarithm; Skorokhod representation; Stochastic integrals; Itô’s formula; Stochastic differential equations
Audience(s) for this book
Students in Mathematics, Physics, Economics, Engineering, and Finance; Financial Institutions; Academic Libraries.
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Winner of the OpenAthens UX Award 2026
Winner of the OpenAthens UX Award 2026
Have an idea on how to improve our website?
Please write us.
© 2026 De Gruyter Brill
Downloaded on 5.3.2026 from https://www.degruyterbrill.com/document/doi/10.1515/9783110307306/html
Scroll to top button