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Stochastic Differential Equations: An Introduction with Applications Paperback – November 4, 2002

4.5 out of 5 stars 6 customer reviews

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Product Details

  • Paperback: 326 pages
  • Publisher: Springer; 5th edition (November 4, 2002)
  • Language: English
  • ISBN-10: 3540637206
  • ISBN-13: 978-3540637202
  • Product Dimensions: 9.3 x 6.2 x 0.8 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #1,958,655 in Books (See Top 100 in Books)

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Top Customer Reviews

Format: Paperback
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.
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Format: Paperback
This is a book I recommend as a TA in a mathematical finance Masters program. It gives a mathematically rigorous presentation of Stocastic Differential Equations without getting bogged down in too much detail, as do many books from a probability/stochastic processes background. It also illustrates the beautiful connection between SDEs and the heat equation. I recommend this book to anyone trying to read Karakas and Shreve for the first time.
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Format: Paperback
This book is excellent if you already know why you want to know the material in it. Then it is concise, to the point, and very well-written. I turn back to it over and over again; my copy is very worn by now.
When I first started reading it, I was not too pleased with it. As a text-book it suffers from not motivating the theory, and not connecting it with parallel approaches. The subtitle mentions applications. Now, what one person considers applications is what the next person considers abstractions. My point of view is truly applied - I want to use SDE's to model real-world phenomena (actually, not financial ones) and are less interested in SDE's per se. So I would have liked more connections with physics (for instance advection-diffusion transport phenomena) and I would have liked the material to be more solidly anchored in general stochastic processes. Nevertheless, I appreciate that the book wouldn't have been as concise, then.
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