Stochastic Processes [Hardcover]

Wolfgang Paul (Author), Jörg Baschnagel (Author)

Book Description

Publication Date: March 7, 2000

From the reviews: "While this book is oriented toward students of physics, it could well be appreciated by a wider mathematical audience […] The text offers a rare opportunity to have a unified and modern treatment of stochastic processes in physics and finance." Bulletin of Mathematics Books

Editorial Reviews

Review

From the reviews:

BULLETIN OF MATHEMATICS BOOKS

"While this book is oriented toward students of physics, it could well be appreciated by a wider mathematical audience…The text offers a rare opportunity to have a unified and modern treatment of stochastic processes in physics and finance."

From the Back Cover

In the canonical theoretical physics course starting with classical mechanics and electrodynamics we become used to deterministic thinking. Even quantum mechanics, although statistical in nature, is often presented from a deterministic point of view. It is not until we get into contact with statistical physics that probabilistic concepts enter into the physical world. Probabilities evolving in time, i.e., stochastic processes, are rarely treated, despite the wide - and interdisciplinary - applicability of the concepts. A diffusion process description applies in the classical Brownian motion problem, in path (-integral) descriptions of non-relativistic quantum mechanics as well as in the celebrated Black-Scholes theory of option pricing in the financial market. This book aims at providing the student with a self-contained introduction (from a physicists point of view) into the basic mathematical concepts of probability theory and stochastic processes and their application in physics and finance. Emphasis is laid onto contrasting the ubiquituous Gaussian distribution and standard Brownian motion with fat-tailed or Levy-stable distributions and Levy-flights, which are at the center of many modern developments in statistical physics as well as in econophysics.

Product Details

• Hardcover: 231 pages
• Publisher: Springer; 1 edition (March 7, 2000)
• Language: English
• ISBN-10: 3540665609
• ISBN-13: 978-3540665601
• Product Dimensions: 9.3 x 6.4 x 0.7 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 3.2 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #3,507,834 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

7 of 7 people found the following review helpful:

5.0 out of 5 stars Excellent coverage of the math and the applications, April 12, 2002

By 

W. P. Gardner (Menlo Park, CA, United States) - See all my reviews
(REAL NAME)   

This review is from: Stochastic Processes (Hardcover)

I wish I had had this book 20 years ago when I first studied stochastic processes in school: I was very interested in them, but did not have a clue about what they were good for.

The book clarifies why we care about Levy distributions as opposed to plain old normal (Gaussian) distributions. I never understood this before. (If you're too lazy to get the book, I will just say it is because of "fat tails". In the world of finance, many people treat the Law of Large Numbers as if it were the Law of Small Numbers, and don't realize how big the samples have to get sometimes to get the effects you want.)

The book would be suitable for undergraduate math majors or graduate students in physics or finance who have enough mathematical background to follow it. It's over the head of people who can't do calculus and under the chin of graduate math students who probably would prefer something more pure and abstract.

3 of 3 people found the following review helpful:

5.0 out of 5 stars Excellent introduction to stochastic processes, November 24, 2002

By A Customer

This review is from: Stochastic Processes (Hardcover)

I like this book very much -- It provides an excellent introduction to the subject of stochastic processes from a physical, as opposed to a mahematical/axiomatic, poit of view. It also provides a good introduction to the very basic aspects of mathematical finance. It includes a rather detailed introduction to Levy processes, which is not easily available in introductory textbooks. I highly recommend this book for physics undergrads who wish to learn the subject. Mathematicians may not really find it to their liking.

0 of 1 people found the following review helpful:

2.0 out of 5 stars nice intention, unfortunately ill delivered, January 7, 2004

By A Customer

This review is from: Stochastic Processes (Hardcover)

The idea of writing a book that introduces the reader to stochastic processes from a more modern viewpoint, leading him from physics through to introductory finance is certainly as good as it is natural as it is timely, if not necessary. Clearly, when we physicists contemplate our standard textbooks by Gardiner, Risken, van Kampen, Mazo, etc... in the light of what fine pedagogical works have been produced by modern finance scholars, they stand there as somewhat old-fashioned.

So the idea by the present authors to produce a more modern approach is certainly most welcome and it should be considered as one of the first steps.

Much as I like and adhere to the idea that a brush-up of the context in which stochastic processes is being taught to phyisicists is needed, I truly cannot forgive the authors for
the ill delivery of the material they present. For instance, there are glaring inaccuracies and errors in the rather critical first pages of chapter 2, relating the basic axioms of probability theory following Kolmogorov's approach. If you do that, then do it properly. Similarly, the confused computation on page 37 demonstrating the equivalence of the Fokker-Planck and Langevin equations is unfortunate to have made it into book form.

The chapter on finance is useful, but as ever so often in econophysics literature, somewhat superficial.

I hope that in a forthcoming second edition the authors will take
care to polish the formal background a bit more, maybe push it a bit further, so as to be able to give a clean definition of martingales, for instance. For a neat, if somewhat terse, presentation of much of the material covered here is still think that Stochastic Processes in Polymeric Fluid by H. C. \"Ottinger is still unsurpassed. Alternatively one can turn his/her attention directly to applied financial derivatives textbooks to pick up the essentials or even stick to the old stuff mentioned above.