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Elements of Stochastic Calculus and Analysis

  • Daniel W. Stroock

Part of the CRM Short Courses book series (CRMSC)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Daniel W. Stroock
    Pages 1-26
  3. Daniel W. Stroock
    Pages 27-56
  4. Daniel W. Stroock
    Pages 57-107
  5. Daniel W. Stroock
    Pages 109-148
  6. Daniel W. Stroock
    Pages 149-202
  7. Back Matter
    Pages 203-206

About this book

Introduction

This book gives a somewhat unconventional introduction to  stochastic analysis.  Although most of the material covered
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.

Keywords

Kolmogorov's equations Ito's approach Markov property Brownian stochastic integration Tanaka's formula Burkholder's inequality semi-martingales Doob-Meyer decomposition theorem Kalman-Bucy filter

Authors and affiliations

  • Daniel W. Stroock
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-77038-3
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-77037-6
  • Online ISBN 978-3-319-77038-3
  • Series Print ISSN 2522-5200
  • Series Online ISSN 2522-5219
  • Buy this book on publisher's site
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