An Introduction to Stochastic Differential Equations by Lawrence C. Evans (PDF)

Description

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).

User’s Reviews

Editorial Reviews: Review … [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. –Mathematical Association of AmericaThese 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 UniversityThis 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 About the Author Lawrence C. Evans , University of California, Berkeley, CA, USA

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Upon examining this book closer I have come to realize that the author DOES in fact state that the prerequisite for the textbook is measure theoretic analysis (ie graduate level analysis). Due to this mistake I have updated my rating.Regardless, this book is on the same level as Oksendal, but much much more detailed on the probability parts. I recommend neither Oksendal or Evans to those that are not mathematically inclined. As others have stated if you have completed your graduate analysis courses then this book is for you.For an “Introductory” book it does not have solutions included in the text which is a huge deterrent for me to recommend this and only this as a primary textbook. Oksendal does include solutions, but his probability section is lacking though. The prerequisites are the same so perhaps together they’d be a good combo?If you have knowledge of measure theory then this book seems like it would be very easy to understand. It is written in a semi modern way meaning that the author does somewhat expand on definitions/theorems/etc. I can recommend it for the target audience.If you do not have knowledge of measure theory then Measure, Integral, and Probability by Capinski and Kopp is a nice place to start. It even has a preliminary section on real analysis topics for those that are not mathematically inclined.If you do not have measure theory or probability as a background then I recommend Calin. If you have knowledge of Probability then I recommend Klebaner or Shreve. If you are looking for a comprehensive graduate level book on the subject then I recommend Baldi. Baldi assumes knowledge of functional analysis and measure theory.

⭐Excellent book! As long as you’ve done your graduate analysis, the proofs are easy to follow and the pace is perfect for a strong introduction! Very clear!

⭐Excellent book

⭐Darn good, comprehensive but not at all laboured. The average second-year maths undergrad should have no difficulty with it.

⭐Excelente libro para introducirse al tema.

⭐

⭐Stochastic differentials are explained in a very systmetically and in an easy way.

⭐Good

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