Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: CRM Short Courses (CRMSC)
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Table of contents (5 chapters)
Keywords
About this book
here 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 of
Malliavin'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 research
mathematicians who may be familiar with many of the topics but want to broaden their understanding of them.
Reviews
“By writing this book the author has shown once again that he is one of the leading masters of modern probability theory. There are all the expectations to believe that the book will be met positively and will be useful and encouraging for both young mathematicians and professionals working in the areas of probability theory and its applications and analysis.” (Jordan M. Stoyanov, zbMATH 1428.60001, 2020)
“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)
Authors and Affiliations
About the author
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).
Bibliographic Information
Book Title: Elements of Stochastic Calculus and Analysis
Authors: Daniel W. Stroock
Series Title: CRM Short Courses
DOI: https://doi.org/10.1007/978-3-319-77038-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-77037-6Published: 07 May 2018
Softcover ISBN: 978-3-030-08354-0Published: 02 February 2019
eBook ISBN: 978-3-319-77038-3Published: 24 April 2018
Series ISSN: 2522-5200
Series E-ISSN: 2522-5219
Edition Number: 1
Number of Pages: XIV, 206