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Stochastic Differential Equations [Print Replica] [Format Kindle]

Bernt Øksendal
4.0 étoiles sur 5  Voir tous les commentaires (2 commentaires client)

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  • ISBN-10 : 3540047581
  • ISBN-13 : 978-3540047582
  • Edition : 6th
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Présentation de l'éditeur

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. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten.

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0 internautes sur 1 ont trouvé ce commentaire utile 
3.0 étoiles sur 5 A standard but not for me 24 juillet 2012
Format:Broché|Achat vérifié
Often a reference to start stochastic calculus, I did not enjoy that book as much - it assumes some prelimanary knowledge I did not have or I forgot, and I did not enjoy the maths presentation. I prefer Shreve "Stochastic Calculus for Finance vol 2" and Mikosh books by far.
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0 internautes sur 1 ont trouvé ce commentaire utile 
5.0 étoiles sur 5 RAS 27 septembre 2011
Par yoman1827
Format:Broché
Le livre que j'ai commandé est bien arrivé, rapidement. Je suis satisfait de cette commande. Vendeur fiable, que je recommande
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Amazon.com: 4.0 étoiles sur 5  23 commentaires
39 internautes sur 39 ont trouvé ce commentaire utile 
4.0 étoiles sur 5 An excellent introduction to stochastic calculus 13 mai 2005
Par J. Lim - Publié sur Amazon.com
Format:Broché
This my recommendation for people who want to learn stochastic calculus for the first time. The virtue of this book is that it keeps matters simple,well grounded, and intuitive enough to hook the newcomers in the subject. Once you get comfortable enough and want to learn technical detail necessary for scholarly research, there are other excellent expositions such as Karatzas and Shreve(1998) and Protter(1990). Some reviews complained that this book is limited to stochastic integration with respect to Brownian motion, but that is precisely why I recommend this book. By starting with Browning motion readers can form concrete mental image of stochastic integration and get ready to stride to more general setting if necessary.

Another virtue of this book is the plenty (easy) exercise problems. Working through them is perhaps the best way to learn stochastic calculus.
17 internautes sur 17 ont trouvé ce commentaire utile 
5.0 étoiles sur 5 overall, it's pretty good 6 mars 2005
Par LB - Publié sur Amazon.com
Format:Broché
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.
18 internautes sur 20 ont trouvé ce commentaire utile 
2.0 étoiles sur 5 Laudable Goal, Poor Execution 14 janvier 2005
Par Applied Math Student - Publié sur Amazon.com
Format:Broché
If calculus is to real analysis then this book is an attempt at filling in _____ is to stochastic analysis. Stochastic analysis is a difficult topic and a simplified introduction with minimal prerequisites is a great goal. However, this book has not fullfilled its promise.

There are a number of complaints to be made about this book. Most importantly is that in his attempt at simplification, Oksendal frequently chooses shedding (important) details over properly motivating a new concept. I found this particularly true in his exposition of generators. The book is poorly also organized: a number of topics are arbitrarily split into different chapters, important ideas hide inside of examples, etc.

While this is not my favorite book by any means, there is currently no replacement for it. Jumping directly into a book like Karatzas&Shreeve can be daunting. I would recommend getting a used copy. Also, previous editions seem to be very nearly identical to the current edition.

I also recommend checking out Rogers&Williams "Diffusions, Markov Process, and Martingales" Vols I&II.
5 internautes sur 5 ont trouvé ce commentaire utile 
5.0 étoiles sur 5 Excellent introduction on Stochastic Differential Equations 8 mai 2007
Par Stephen Tam Kwok Keung - Publié sur Amazon.com
Format:Broché
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.
11 internautes sur 13 ont trouvé ce commentaire utile 
3.0 étoiles sur 5 Too dense and theoretical for beginners 1 février 2006
Par ger128 - Publié sur Amazon.com
Format:Broché
The exposition is correct and concise, but too dense for someone without an extensive mathematical background.

I would much rather recommend Shreve's Stochastic Calculus for Finance II. Though longer, it is much more well-motivated and gives you a more intuitive feel for the concepts as opposed to Oksendal's full-on theoreical treatment.
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