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Stochastic Differential Equations: An Introduction with Applications (Universitext) | 
 enlarge | Author: Bernt Oksendal
Publisher: Springer
Category: Book
List Price: $49.95
Buy New: $33.00
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Rating:  22 reviews
Sales Rank: 38159
Media: Paperback
Edition: 6th
Pages: 374
Number Of Items: 1
Shipping Weight (lbs): 1.3
Dimensions (in): 9.1 x 6.1 x 0.9
ISBN: 3540047581
Dewey Decimal Number: 519.2
EAN: 9783540047582
Publication Date: June 12, 2007
Availability: Usually ships in 1-2 business days
Condition: International edition. Paperback. Different cover but same text .
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Product Description
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided.
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| Customer Reviews: Read 17 more reviews...
 overall, it's pretty good March 6, 2005
LB (New York, NY)
13 out of 13 found this review helpful
It's actually a very good book if you need to learn the topic quickly, armed with a good background in probability theory you will have no difficulty getting through the first 1/3 of the book and gain a working knowledge of SDEs, Ito calculus etc. IT is at times concise in the sense that it lacks motivation etc., but the exposition is such that this presents no major hurdles, as the proofs are clear and short, there are very few errors, except the ones mentioned by the reviewer below, which I should double-check again because I didn't really use this book for its feynman-kac formula (there are better books out there for that). An excellent feature of the book, for those wanting examples from physics and other applied fields, are the problems at the end of chapters. You should definitely give it a try, many of them present the necessary motivation (solutions are at the end of the book). Despite the criticism below, which I consider minor (i.e. it could easily be fixed in a subsequent edition), it is a standard textbook for SDEs, which many respectable mathematicians recommend. Books should be judged by how many times they are quoted by experts, and this book certainly has been cited many times.
Simple, but rigorous book August 17, 2000
Alex Levin (New York)
26 out of 27 found this review helpful
This a perfectly written book on stochastic calculus, especially needed for junior (but rising!) financial quants. All themes are carried out with a profound pedagogical talent. For a practitioner, the book loses nothing to Karatsas and Shreve, but is a much shorter, simpler and joyable reading. Yet, it is a systematic text book that covers most classical results with (important!) accessible proofs. For example, the Kolmogorov equations (forward and backward) are derived, not just stated as in most other texts, Girsanov's theorem is relatively well covered (although the author has not demonstrated its computational side well enough, but this is a common disease). Ideas are illustrated by practical problems (including those from quantitative finance). What I also liked, Oksendal's SDE theory is much closer to "differential equations", than what is often presented by probabilists. A must for every practitioner who works with stochatic processes.
Clear and Straight-forward August 21, 2005
CSA (Chicago, IL)
3 out of 3 found this review helpful
From the cover, one can infer that this book means business. Some books still try to be artistic to attract audiences, whereas this book does away with a creative cover altogether. How often do you see that a book's cover contains five sample paths of a geometric Brownian Motion? Inside, Oksendal writes very clearly and uses the same format throughout. Although the topic is not the easiest to understand, you can acquire the skills that would allow you to gain sufficient knowledge of stochastic differential equations. He starts off with a good introduction and then moves on to the main topics. His applications to finance are also very useful for those in the field. A word of caution is that you would need a decent background in mathematics to read this book, but it is easier than Shreve or Karatzas and Shreve.
A very good book! July 5, 2007
PST (Eislingen Deutschland)
2 out of 2 found this review helpful
I read this book after I had read Karatzas' and Shreve's book "Stochastic Calculus..." and it is probably better to do it the other way round. The mathematical prerequisites are not high, however a good intuitive understanding of measure theory is probably necessary. The pace of the book is leasurely, the proofs are such, that pencil and paper is rarely needed, however no rigor is lost.
The book quickly moves to interesting applications of the theory, which is motivated very well.
It contains a few typographical errors, mostly in the last chapter, and mostly of a harmless nature.
With the necessary mathematical background, it seems to be an ideal introduction to this highly interesting topic of stochastic differential equations!
Excellent introduction on Stochastic Differential Equations May 8, 2007
Stephen Tam Kwok Keung (Hong Kong)
2 out of 2 found this review helpful
A well written book in Mathematics
Stochastic Differential Equations is a branch of mathematics. This book is not just for financial derivatives analysis or modeling. Oksendal first introduces the subject by raising a few stochastic problems (population growth; electric charge in RLC circuit; filtering problems, Dirichlet problems; asset management; optimal portfolio and options pricing) in the first chapter. The subsequent chapters develop notions and techniques which are able to solve wide varieties of stochastic problems (not just those mentioned in the first chapters). The arrangement is impressive in particular for readers who have no previous knowledge about the subject. The readers at least know the target for developing the techniques and would not lose the way when manipulating tons of symbols. Hints and answers to selected problems are invaluable to students for self-study.
To achieve a sound background on stochastic equations is extremely important especially in quantitative finance. It is not an easy job however. QF students may consider going through this book before seriously take Shreve's books on Stochastic Calculus for Finance.
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