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An Introduction to Stochastic Differential Equations
 
Lawrence C. Evans University of California, Berkeley, Berkeley, CA
Softcover ISBN:  978-1-4704-1054-4
Product Code:  MBK/82
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
eBook ISBN:  978-1-4704-1612-6
Product Code:  MBK/82.E
List Price: $39.00
MAA Member Price: $35.10
AMS Member Price: $31.20
Softcover ISBN:  978-1-4704-1054-4
eBook: ISBN:  978-1-4704-1612-6
Product Code:  MBK/82.B
List Price: $84.00 $64.50
MAA Member Price: $75.60 $58.05
AMS Member Price: $67.20 $51.60
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An Introduction to Stochastic Differential Equations
Lawrence C. Evans University of California, Berkeley, Berkeley, CA
Softcover ISBN:  978-1-4704-1054-4
Product Code:  MBK/82
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
eBook ISBN:  978-1-4704-1612-6
Product Code:  MBK/82.E
List Price: $39.00
MAA Member Price: $35.10
AMS Member Price: $31.20
Softcover ISBN:  978-1-4704-1054-4
eBook ISBN:  978-1-4704-1612-6
Product Code:  MBK/82.B
List Price: $84.00 $64.50
MAA Member Price: $75.60 $58.05
AMS Member Price: $67.20 $51.60
  • Book Details
     
     
    2013; 151 pp
    MSC: Primary 65; 60

    This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive “white noise” and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Itô stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing.

    This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

    Readership

    Undergraduate and graduate students interested in probability theory and stochastic differential equations.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Introduction
    • Chapter 2. A crash course in probability theory
    • Chapter 3. Brownian motion and “white noise”
    • Chapter 4. Stochastical integrals
    • Chapter 5. Stochastic differential equations
    • Chapter 6. Applications
    • Appendix
    • Exercises
    • Notes and suggested reading
  • Reviews
     
     
    • These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic.

      Srinivasa Varadhan, New York University
    • This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability.

      George Papanicolaou, Stanford University
    • This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically.

      Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch
    • ... [A]n interesting and unusual introduction to stochastic differential equations...topical and appealing to a wide audience. ... This is interesting stuff and, because of Evans' always clear explanations, it is fun too.

      MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2013; 151 pp
MSC: Primary 65; 60

This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive “white noise” and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Itô stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing.

This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

Readership

Undergraduate and graduate students interested in probability theory and stochastic differential equations.

  • Chapters
  • Chapter 1. Introduction
  • Chapter 2. A crash course in probability theory
  • Chapter 3. Brownian motion and “white noise”
  • Chapter 4. Stochastical integrals
  • Chapter 5. Stochastic differential equations
  • Chapter 6. Applications
  • Appendix
  • Exercises
  • Notes and suggested reading
  • These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic.

    Srinivasa Varadhan, New York University
  • This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability.

    George Papanicolaou, Stanford University
  • This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically.

    Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch
  • ... [A]n interesting and unusual introduction to stochastic differential equations...topical and appealing to a wide audience. ... This is interesting stuff and, because of Evans' always clear explanations, it is fun too.

    MAA Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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