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SoftcoverISBN:  9781470410544 
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Softcover ISBN:  9781470410544 
Product Code:  MBK/82 
List Price:  $37.00 
MAA Member Price:  $33.30 
AMS Member Price:  $29.60 
Sale Price:  $22.20 
eBook ISBN:  9781470416126 
Product Code:  MBK/82.E 
List Price:  $34.00 
MAA Member Price:  $30.60 
AMS Member Price:  $27.20 
Sale Price:  $20.40 
Softcover ISBN:  9781470410544 
eBookISBN:  9781470416126 
Product Code:  MBK/82.B 
List Price:  $71.00$54.00 
MAA Member Price:  $63.90$48.60 
AMS Member Price:  $56.80$43.20 
Sale Price:  $42.60$32.40 

Book Details2013; 151 ppMSC: 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).ReadershipUndergraduate 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


Additional Material

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 nonspecialists 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


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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).
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 nonspecialists 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