Item description for Basic Stochastic Processes by Zdzisaw Brzezniak & Tomasz Zastawniak...
This book is a final year undergraduate text on stochastic processes, a tool used widely by statisticians and researchers working in the mathematics of finance. The book will give a detailed treatment of conditional expectation and probability, a topic which in principle belongs to probability theory, but is essential as a tool for stochastic processes. Although the book is a final year text, the author has chosen to use exercises as the main means of explanation for the various topics, and the book will have a strong self-study element. The author has concentrated on the major topics within stochastic analysis: Stochastic Processes, Markov Chains, Spectral Theory, Renewal Theory, Martingales and It Stochastic Processes.
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Est. Packaging Dimensions: Length: 0.75" Width: 6.75" Height: 9.5" Weight: 0.9 lbs.
Release Date Sep 6, 2000
ISBN 3540761756 ISBN13 9783540761754
Reviews - What do customers think about Basic Stochastic Processes?
Superb if you know some measure theory Dec 3, 2005
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.
Excellent for helping with the theory May 14, 2005
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.
An excellent starter book : pre-SDEs Feb 3, 2004
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.
Great Mid-Level Intro Dec 3, 2003
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.
Stochastic Processes Nov 7, 2002
This is an excellent book for anyone who can use maths at degree level. Forget complex analysis, this is far and away the best book for a good subject...