Introduction to Stochastic Calculus with Applications [Hardcover]

Fima C. Klebaner (Author), Klebaner Fima C (Author)

Book Description

Publication Date: September 1, 1999 | ISBN-10: 186094129X | ISBN-13: 978-1860941290

This is a concise introduction to stochastic calculus with some of its applications in mathematical finance, engineering and the sciences. Applications in finance include pricing of financial derivatives, such as options on stocks, exotic options and interest rate options. The filtering problem and its solution is presented as an application in engineering. Population models and randomly perturbed equations of physics are given as examples of applications in biology and physics. Only a basic knowledge of calculus and probability is required for reading this book. The text gradually takes the reader from a fairly low technical level to a sophisticated one. Heuristic arguments are often given before precise results are stated, and many ideas are illustrated by worked-out examples. Exercises are provided at the end of chapters to help test the readers' understanding.

Editorial Reviews

Review

"...hard to find books on stochastic analysis which present such a wide spectrum of results with relatively modest prerequisites" -- Mathematical Reviews, 2002

It provides a good introduction to stochastic analysis, leaving out several of the more technical proofs. -- Zentralblatt MATH

From the Author

I wanted to write a book that would introduce stochastic calculus, which is a very technical subject, in a simpleminded way. The book is a mathematical text, but the entrance level is lower than other rigorous stochastic calculus books. It is is suitable for advanced undergraduates, graduates and researchers in probability & statistics and mathematical finance.

Product Details

• Hardcover: 336 pages
• Publisher: World Scientific Publishing Company (September 1, 1999)
• Language: English
• ISBN-10: 186094129X
• ISBN-13: 978-1860941290
• Product Dimensions: 8.8 x 6.3 x 0.9 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 4.2 out of 5 stars  See all reviews (11 customer reviews)
• Amazon Best Sellers Rank: #3,132,719 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

19 of 20 people found the following review helpful:

5.0 out of 5 stars Perfect!, October 6, 1999

By A Customer

This review is from: Introduction to Stochastic Calculus with Applications (Hardcover)

I had a course of stochastic processes four years ago. A month ago I needed to revive my faded (and very weak) knowledge of stochastic calculus and to learn more as much and as fast as I can. I checked a lot of books about stochastic calculus and financial math, but this book is the best one (of those which I saw) which gives a simple but a rigorous treatment of the subject. If something is not proved then for the case there is an explicit reference to a text. I believe if you have some knowledge of probability it is a very good book to start to learn stochastic calculus.

16 of 17 people found the following review helpful:

5.0 out of 5 stars excellent introductory text, January 4, 2001

A Kid's Review

This review is from: Introduction to Stochastic Calculus with Applications (Hardcover)

This is an excellent book on elementary stochastic calculus that is application oriented, and does not get bogged down too much with measure theory. I do not understand the comments of other readers. If they do not have a certain background in real analyis, and some probability theory how can they attempt to learn stochastic calculus. There is no magic book that will teach you stochastic calculus if you don't have some "basic" background in math.To repeat, this book is very good for beginners.

9 of 9 people found the following review helpful:

4.0 out of 5 stars A good book with yet misleading intro, March 14, 2003

By A Customer

This review is from: Introduction to Stochastic Calculus with Applications (Hardcover)

I have to agree with one of the earlier reviewers who rates the book only 3-star. As a reader from engineering background who is determined to grasp the gist of stochastic calculus, I found at the beginning this book hard to carry on. It is only after taking on some readings about theoretical probability and measure theory that I find this book enjoyable. Thus, the statement of 'only a basic knowledge of calculus and probability is required' in the preface is misleading. One has to realize what is considered 'basic knowledge' for mathematicians may not be basic for engineerings, and vice versa.

But, this is indeed an excellent book on the subject without burdening the readers with every rigorous proofs. I would have rated it 5-star if not for the misleading statement. As long as one has a basic knowledge in real analysis, indeed very basic, one will find this book highly enjoyable.