Introduction To Stochastic Calculus With Applications (3Rd Edition)

This book is easy to read and comprehensive.

I have indeed come around to this book. The first chapter lacks exercises and has fact after fact thrown at you (with motivation). Chapter two lacks exercises as well unfortunately, but still flows. Motivations are stated or can be extrapolated. Actually, I would prefer for the first chapter to be dissolved into the rest of the book altogether and introduced when needed. I think it would be fresh in the readers mind right before it is required.The theory is developed at the beginning of each section and then the author gives an actual real example for the reader to work through. Usually the example leads into the following theorem and the text does feel like it flows well. Although probability is assumed, I would still like all notation clearly defined either in text or a notation page somewhere in the appendix. For instance ~ is never clearly defined. It is only hinted at that it means "has the distribution".From the third chapter onwards there are exercises and solutions to some of the problems in the back of the book. It continues to have many examples and is written in a modern way. It offers explanations further than just definitions theorems and proofs.I have definitely learned to appreciate this book and I can see someone learning from this book with no background on the subject. I would recommend just taking the first chapter for what it is.The first two chapters are in dire need of exercises. If the author is reading this then I humbly request that you expand upon the second chapter to make the text "complete". I refer anyone that doesn't have a probability background to the GREAT text by Calin.For beginners I would recommend reading at least chapter one of Shreve, chapter 2 of Calin, or reading Mikosch in its entirety. Mikosch is an easy read that serves as a great prerequisite to the subject no matter what book you decide to learn from.

As an aerospace engineering grad student with some real analysis background but not formal training in stochastic calculus, this textbook is ideal for self study. Fundamental concepts that are brushed over (such as the similarities/differences of Riemann, Stieltjes, and Lebesgue integrals) or altogether ignored (such as jump processes) by the classic Oksendal text (Stochastic Differential Equations: An Introduction with Applications) are covered in detail.While Oksendal devotes just three pages to the Brownian motion process, which is fundamental to the construction of the Ito integral, Klebaner takes half of chapter 3 and all of chapter 4 explore the Brownian motion process, develop intuition about its properties, and carefully explain how it is used in the construction of the Ito integral.In terms of mathematical preliminaries, Oksendal's text largely assumes the reader is well versed in measure theoretic probability. The Oksendal text is woefully brief in its review of mathematical background needed to dive into the text (14 pages, 6 of which are exercises). The Klebaner text devotes 54 pages to review, providing an excellent opportunity to not only provide the reader with familiarity of the author's notation, but also to tie together concepts from real analysis, probability theory, and differential equations that the reader has probably not seen together in a single setting.Finally, the Klebaner text is far more navigable. The first 11 pages of the 6th edition of the Oksendal text consist of various forwards, dedications, and prefaces; this arrangement makes it rather difficult to get to the table of contents. Oksendal's table of contents are, in a word, terse. Klebaner's table of contents are, pleasantly, at the beginning of the text and have far more detail.I find Klebaner's text covers more material, contains much higher quality exposition, is far more self-contained, and is much easier to navigate than the widely used Oksendal text.

Very enjoyable - buy it.

Very clean

I still remember the time that I read the first edition of this book. The second edition gets a great improvement but we still want it more. The HJM and BGM models are the most important parts of this one that you should participate in and understand a lot. The term structure of interest rate is only the factor for the whole stochastic process we use in the finance. There are always three factors: interest rate for the discount no matter it is stocastic or deterministic, stochastic time we care, and the price the underlying moves we have to know. The book makes those situations in a better shape. I have to say the man from China seems to give some advice but it just contributes minor to the latest 3rd edition. We still look forward a big progress on those two HJM and BGM modellings. It is a little disappointment to me for the new edition. I still remember the time I learn the second edition in the graduate school. It is a time to explore those stories with the latest version written by John Hull. It is a good pair or a good couple for the student who wants to know the financial engineering and financial mathematics better. Just as Chen,Ren-Raw (NY,NY) once said, it is the financial meathematics instead of mathematical finance. It is the subject provided for those ones who fall in love with finance instead of loving mathematics. It will cost you a lot of time to know the difference. And I just did it!! Not matter what people say, it is an introduction book but you still need to know some fundamental issues like basic statistical stochastic processes(Sheldon Ross), mathematical statistics(Roussas) and probability(Durrett). Of course if you can read the book written by Ren-Raw Chen, you may find out it is a good companion with this one. To allow me to say that Mr. Klebaner does help me a lot on the issue of stochastic calculus. It is worth to have one and take a lot of notes on it. Please read it over and take all those questions personally. Then you will find out what a beautiful world of financial stochastic calculus can be.

I took this course in fall of 1989. At that time, i used the book of Ioannis Karatzas but i found this book very interesting . And i like the style in which the book was writing, easy to read with great applications

Excelente

Good

Speedy Delivery and as described. Book is good although it lacks examples and some more transparency over calculations. Good to start understanding basic Stochastic processes