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Basic Stochastic Processes: A Course Through Exercises (Springer Undergraduate Mathematics Series) Paperback – 26 Jul 2000


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Product details

  • Paperback: 236 pages
  • Publisher: Springer; 1st ed. 1999. Corr. 3rd printing 2000 edition (26 July 2000)
  • Language: English
  • ISBN-10: 3540761756
  • ISBN-13: 978-3540761754
  • Product Dimensions: 17.8 x 1.4 x 23.5 cm
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: 138,760 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

This book fulfils its aim of providing good and interesting material for advanced undergraduate study.

The Times Higher Education Supplement

This is probably one of the best books to begin learning about the sometimes complex topic of stochastic calculus and stochastic processes from a more mathematical approach. Some literature are often accused of unnecessarily complicating the subject when applied to areas of finance. With this book you are allowed to explore the rigorous side of stochastic calculus, yet maintain a physical insight of what is going on. The authors have concentrated on the most important and useful topics that are encountered in common physical and financial systems

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Most Helpful Customer Reviews

8 of 8 people found the following review helpful By Surf/Bike on 8 Feb 2003
Format: 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 By Palle E T Jorgensen on 19 Mar 2010
Format: 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 By Gaurav Saroliya on 28 Nov 2005
Format: 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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9 of 12 people found the following review helpful By A Customer on 24 Jun 1999
Format: 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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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 14 reviews
36 of 39 people found the following review helpful
Excellent for helping with the theory 14 May 2005
By reader - Published on Amazon.com
Format: Paperback
After reading the few bad reviews for this book, I thought I should explain this book. This book is excellent in helping you with the theory; but don't be fooled--Pure Stochastic Process theory is extremely hard and mathematically abstract. I consider this book superb in its attempt to help others learn the difficult theory. I've noticed in the past that certain people who cannot handle mathematical theory or who just want to obtain knowledge instantly will tend to bash the mathematics itself (and mathematicians) rather than admit that theory really is hard for them. This book is not for the weak who want to dodge the theory and just get to the punchlines. Also, it does NOT go over applications for finance majors. Instead it is intended for those willing and able to handle mathematical theory but still needing guidance through the fundamentals that will lead them to a better understand of stochastic processes. This book is not all encompassing. It is basic and introductory, but it does require you to have mathematical maturity with the theory of limits including the infinite sequences of sets.
14 of 15 people found the following review helpful
Superb if you know some measure theory 3 Dec 2005
By Gaurav Saroliya - Published on Amazon.com
Format: Paperback
This book is a boon for the non-mathematician enthusiast, 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, this book certainly reduces enormously the cost of entry into the extremely difficult world of stochastic analysis for the non-mathematician. The prerequisites include some knowledge of measure-theoretic ideas like Borel sets and Lebesgue measure. For the later chapters, some knowledge of intermediate measure-theoretic results like monotone & dominated convergence theorems, Fatou's lemma, etc will be required. Apart from these, the book demands little else in the way of prerequisites. Particularly, someone without a detailed knowledge of functional analysis will survive this book but not the likes of Karatzas and Shreve's Brownian Motion and Stochastic Calculus.
13 of 15 people found the following review helpful
An excellent starter book : pre-SDEs 3 Feb 2004
By A Customer - Published on Amazon.com
Format: Paperback
I've worked through this book. It's an excellent introduction
to stochastic processes, sigma-algebras and quite an
expanded introduction to conditional expectation.
This nicely expands conditioning on an event, to conditioning
on (in order) a discrete rv, a continuous rv, a sigma-algebra
generated by a rv, and finally to just a sigma-algebra.
Only the Martingale Inequalities chapter seems a bit
isolated but is of course used later.
This book is Chap 2 of Oksendal (Mathematical Preliminaries).
For a PhD in maths/mathematical finance this is maybe a week
or twos work. It looks like a terms course for undergrads.
6 of 6 people found the following review helpful
Understandable 12 Dec 2001
By A Customer - Published on Amazon.com
Format: Paperback
The book indeed does not contain the material I thought it would: I thought I get to know a huge amount of different stochastic processes, maybe even learn how to solve stochastic differential equations. Nevertheless, I have learnt things that were inaccessible to me before (e.g. what's the idea behind a filtration?), therefore I rate the book at 5 stars. A very good and understandable introduction.
6 of 6 people found the following review helpful
Great Mid-Level Intro 3 Dec 2003
By A Customer - Published on Amazon.com
Format: Paperback
This book fills the gap between the too basic and quite advanced accounts of stochastic calculus. Great for someone with solid--but not graduate level--math background.
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