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Brownian Motion and Stochastic Calculus (Graduate Texts in Mathematics)
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Binding: Paperback
Dewey Decimal Number: 530.475
EAN: 9780387976556
Edition: 2nd
ISBN: 0387976558
Label: Springer
Manufacturer: Springer
Number Of Items: 1
Number Of Pages: 470
Publication Date: August 25, 2004
Publisher: Springer
Studio: Springer
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Editorial Review:This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization).
This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large number of problems and exercises.
Customer Reviews
Average Rating: 
Rating:  - Excelent
This is a great book. By far, the best I have red about stochastic analysis
Rating: - A Superb Book
I found this book to be an excellent introduction into the subject matter. A good background in measure theoretic probability theory definitely helps, but even without much background, it is possible to understand all, but the finest measure theoretic points (I am a hobby mathematician with an engineering background, and I simply used the book "Probability Theory" by Laha & Rohatgi to learn what was needed about measure theory).
It is amazing, how the authors motivate, what they are doing ... Read More
Rating:  - Massive Exercise to the Reader
This book isn't really the place to start learning about stochastic calculus. Get Oskendal's Stochastic Differential Equations: An Introduction with Applications for this.
Even to the prepared reader, this book is exasperating. It is as if the authors came up with an excellent outline for an advanced treatment of this topic. Then they realized that to do all of the material justice, they'd need to have not one, but two 400 page volumes. Their publisher must have balked at that idea, so ... Read More
Rating:  - A Must
If you want to learn about stochastic calculus, this is the gold standard. Certainly a challenge, but if you can answer all the questions posed in the book you will have a very thorough knowledge of BM, stochastic integration with respect to BM, SDE's, and the SDE/PDE relationship.
While this is a great book, I do have a couple complaints. First of all there a points in the book where overly complicated notation can obscure the point being made. Secondly, since the book does not cover semimartingale ... Read More
Rating: - The best introduction
The theory of Brownian motion is ubiquitous in physics and mathematics, and has recently become very important in mathematical finance and network modeling. The observation of the irregular movement of pollen suspended in water by Robert Brown in 1828 led Albert Einstein to formulate a theory for Brownian motion. In this book the authors outline rigorously the theory of Browian motion. Their logic is impeccable, and the content is fascinating reading, even to those very experienced in the subject.
The authors ... Read More
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