Save 40% on books and eBooks in Engineering & Materials Science or in Social & Behavioral Sciences!

CRM Short Courses

Elements of Stochastic Calculus and Analysis

Authors: Stroock, Daniel W.

Free Preview
  • Often written in a more essay form, the text contains many unique insights into the topic
  • Broadens understanding of the material for advanced grad students and research mathematicians
  • Includes unique and challenging exercises in each chapter
see more benefits

Buy this book

eBook  
  • ISBN 978-3-319-77038-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Hardcover  
  • ISBN 978-3-319-77037-6
  • Free shipping for individuals worldwide
Softcover  
  • ISBN 978-3-030-08354-0
  • Free shipping for individuals worldwide
About this Textbook

This book gives a somewhat unconventional introduction to  stochastic analysis.  Although most of the material coveredhere has appeared in other places, this book attempts to explain the core ideas on which that material is based.  As a consequence, the presentation is more an extended mathematical essay than a ``definition,lemma, theorem'' text.  In addition, it includes several topics that are not usually treated elsewhere.  For example,Wiener's theory of homogeneous chaos is discussed, Stratovich integration is given a novel development and applied to derive Wong and Zakai's approximation theorem, and examples are given of the application ofMalliavin's calculus to partial differential equations.  Each chapter concludes with several exercises, some of which are quite challenging.  The book is intended for use by advanced graduate students and researchmathematicians who may be familiar with many of the topics but want to broaden their understanding of them.

About the authors


Daniel W. Stroock is Professor Emeritus of Mathematics at MIT. Professor Stroock's research interests focus on probability theory and stochastic processes.  Stroock (with S. Varadhan) was awarded the Leroy P. Steele Prize for seminal contributions to research in stochastic equations. In 2007, Stroock received an Honorary Fellowship at Swansea University, Wales, and in 2004 selected to be Foreign Member of the Polish Academy of Arts and Sciences. Professor Stroock is a Fellow of the American Academy of Arts and Sciences (1991), and a Member of the National Academy of Sciences (1995). Professor Stroock has made many contributions to pedagogical literature, among these include: An Introduction to Markov Processes" (GTM 230),  "Essentials of Integration Theory for Analysis" (GTM 262), "Multidimensional Diffusion Processes" (Classics in Mathematics).

Reviews

“This is a high level book suitable for an advanced graduate level course, but can be useful for research mathematicians as well.” (Tamas Szabados, Mathematical Reviews, July, 2019)

Table of contents (5 chapters)

Table of contents (5 chapters)
  • Kolmogorov’s Equations

    Pages 1-26

    Stroock, Daniel W.

  • Itô’s Approach

    Pages 27-56

    Stroock, Daniel W.

  • Brownian Stochastic Integration

    Pages 57-107

    Stroock, Daniel W.

  • Other Theories of Stochastic Integration

    Pages 109-148

    Stroock, Daniel W.

  • Addenda

    Pages 149-202

    Stroock, Daniel W.

Buy this book

eBook  
  • ISBN 978-3-319-77038-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Hardcover  
  • ISBN 978-3-319-77037-6
  • Free shipping for individuals worldwide
Softcover  
  • ISBN 978-3-030-08354-0
  • Free shipping for individuals worldwide
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Elements of Stochastic Calculus and Analysis
Authors
Series Title
CRM Short Courses
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-77038-3
DOI
10.1007/978-3-319-77038-3
Hardcover ISBN
978-3-319-77037-6
Softcover ISBN
978-3-030-08354-0
Series ISSN
2522-5200
Edition Number
1
Number of Pages
XIV, 206
Topics