Stochastic Differential Equations: An Introduction with Applications (Universitext)

The coverage of topics for an applied focus, or as a taster for pursuits more pure in the world of SDEs, is excellent. If more (e.g. analysis level) rigour is needed, one can supplement study with Durrett, or Rogers & Williams. What this book does well (which I originally hadn't appreciated) is to string together the topics well, and pitch them at a level which is not too abstruse. This is no small feat! Also, the exercises cover quite a lot of ground. This could be a good or bad thing depending on your predisposition.

A really good book for anyone who is looking for an introduction to SDEs or some more advanced stuff and is suitable for self-study. The book contains detailed solutions of selected exercises. I would recommend the seller to anyone. The book was sent at the same day as I made the order.

A bit basic for advanced calculous, a bit complicated for newcomers, but if you are using stochastic calculous every now and then and need to stay "fresh" it's perfect.

Practical and good explanation with many topics considered (karman filter, stochastic control, ...) but the presentation is abysmal and can be significantly improved.

great

There are two types of books one finds in the field of mathematics --introductory books that aim to get the reader acquainted with the topic and drop rigour and rigorous treatises that build upon previously gained sketchy knowledge and fill in the gaps. This book defines its own category --an introductory book which assumes the reader is an expert already and drops the rigour by redirecting the reader to more advanced texts. Therefore, this book is useless for both types of readers. The book is primarily written to be as obtuse and intimidating as possible. Sadly, in some mathematics departments, being understandable and accessible makes you an outcast. The author has therefore decided to impress his friends and write a terse textbook that makes the reader go through the chapter 7-8 times in order to just understand what has been written in the equations. A better textbook can explain the same thing in precise language without dropping the rigour but then it would not sound smart. My advice for anyone begining to enter this field would be to avoid this book. There are far more accessible textbooks and rigorous ones than this book.

Perfect

This book is very well placed on the difficulty scale. It does require some mathematical background (mainly probability and measure theory) but it does not leave the reader on their own with the difficult material. It is a textbook with a lot of comments, examples and worked exercises and it is very practical as well (it the sense that unlike some other books it is not a theory of everything that can be said about the subject but the author selected the most important results and presented them in a very attainable form). The reader may sometimes have an impression that some explanations could be more detailed but I found those little gaps an enjoyable exercise when reading.

Nach einer Grundlagenvorlesung über Wahrscheinlichkeitstheorie eignet sich das Puch perfekt zum Selbststudium, da sogar Lösungsansätze mit aufgezeigt werden. Das Buch hat 5 Sterne verdient und kann als Standardwerk in diesem Bereich angesehen werden.

testo molto didattico: l'autore non trascura il rigore matematico senza appesantire il testo di dimostrazioni (si rimanda alle referenze o all'appendice). Il filo del discorso è fluido e continuo, in modo da non perdere mai il fine ultimo, caratteristica che fa del libro anche un eccellente testo per autodidatti. La ricchezza di esercizi, svolti e non, alla fine di ogni capitolo aiuta il lettore ad una più profonda comprensione degli argomenti. L'approccio alla materia è generale ma non mancano negli ultimi capitoli applicazioni, soprattutto nel campo principe della matematica finanziaria. Consigliato soprattutto a tutti coloro che muovono i primi passi nel campo del calcolo stocastico e in genere a chi vuole con sé una pietra miliare dell'argomento.

This is a very good introduction on the subject, with interesting examples and a well-constructed theory. A must in the basic of stochastic calculus.

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This book is offers an excellent introduction to SDE but limiting the text to integration w.r.t Brownian motion. The book is structured by first introducing 6 problems which are solved using the concepts and theory discussed in the chapters that follow. This is an excellent pedagogical tool, that is used to focus the mind on applications, in order to understand the abstract concepts discussed. The level of mathematics is moderate in difficulty with some proofs omitted (but with references included) for the sake of not veering away too far from the main concepts (and the need to introduce further preliminaries to understand the proof). There are also exercises included (with some solutions and hints) that allows the reader to solidify the understanding and applications. The follow-up text is commonly the Karatzas and Shreve book,though its level of difficulty is substantially higher than this text.