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8 of 8 people found the following review helpful
5.0 out of 5 stars Solid Introduction to applied probability and stochastics, 8 Feb 2003
This review is from: Basic Stochastic Processes: A Course Through Exercises (Springer Undergraduate Mathematics Series) (Paperback)
I have extensively used this book for a course on stochastic analysis...The exercises and examples really helped to fully understand the theory. I suggest to read it in conjunction with D. Williams book or Jacod-Protter. The book assumes, anyway, some prerequistes on applied probability, even if the first two chapters are devoted to fix some of these concepts in view of the later chapters.
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1 of 1 people found the following review helpful
5.0 out of 5 stars clear explanations, 19 Mar 2010
By 
Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
(REAL NAME)   
This review is from: Basic Stochastic Processes: A Course Through Exercises (Springer Undergraduate Mathematics Series) (Paperback)
Well motivated; well explained; easy to understand! A great read; and still offering readers getting a deeper understanding! There are a number of reasons for this book: An understandable presentation of tools from probability and stochastic processes is especially timely.
With clear explanations, and with lots of examples and illustrations!
A useful first book, before turning to more specialized presentations!
While the subject has a long history and a multitude of applications, there is more recent buzz: It has been suggested that the recent turmoil in financial markets may be caused in part by poor understanding on the part of traders of the mathematical models for derivative trading.
The mathematical tools are widely used, but probably a lot less widely understood!

A bit of history: Stochastic processes is a theory started more than a hundred years ago (1900, Louis Bachlier, a Paris-PhD thesis under Poincare), then Albert Einstein's 1905 discovery of Brownian motion, Norbert Wiener's path-space integral (the 1920ties), K. Ito's integral & formula (the 1940ties) and Paul Samuelson-Merton-Black-Scholes 1974, a stochastic differential equation for option pricing: All mathematical tools devised for the purpose of predicting uncertain outcomes in the world around us: in financial engineering; in physics (quantum mechanics, diffusion & thermodynamics); in biology, and in other parts of our experience.
Review by Palle Jorgensen, March 2010.
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4 of 5 people found the following review helpful
5.0 out of 5 stars Superb support if you know some measure theory, 28 Nov 2005
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This review is from: Basic Stochastic Processes: A Course Through Exercises (Springer Undergraduate Mathematics Series) (Paperback)
This book is a boon for the non-mathematician financial quant, providing the reader knows some concepts of measure-theoretic probability. The idea of conditional expectation, which is the backbone of the theory of stochastic processes, is developed in considerable detail, which provides an excellent preparation for the study of martingales, Markov chains and Brownian motion in the subsequent chapters. There are numerous exercises scattered all over the chapters with full solutions at chapter ends. Although it does not provide the level of detail that one would get in a book like Oksendal, it certainly reduces the cost of entry into the difficult world of stochastic analysis for the non-mathematician. The only prerequisite is some knowledge of measure-theoretic ideas like Borel sets and Lebesgue measure.
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8 of 11 people found the following review helpful
4.0 out of 5 stars Very good introduction to stochastics, 24 Jun 1999
By A Customer
This review is from: Basic Stochastic Processes: A Course Through Exercises (Springer Undergraduate Mathematics Series) (Paperback)
The book fulfils it title - I think it's a very good introduction to this area. It grounds stochastic processes in probability, and is consequently self-contained. The examples and exercises (with worked solutions) really helped me understand the theory.
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