Probability with Martingales

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Cambridge University Press, Feb 14, 1991 - Mathematics - 251 pages
8 Reviews
Probability theory is nowadays applied in a huge variety of fields including physics, engineering, biology, economics and the social sciences. This book is a modern, lively and rigorous account which has Doob's theory of martingales in discrete time as its main theme. It proves important results such as Kolmogorov's Strong Law of Large Numbers and the Three-Series Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions. A distinguishing feature is its determination to keep the probability flowing at a nice tempo. It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals; and it assumes certain key results from measure theory in the main text. These measure-theoretic results are proved in full in appendices, so that the book is completely self-contained. The book is written for students, not for researchers, and has evolved through several years of class testing. Exercises play a vital rôle. Interesting and challenging problems, some with hints, consolidate what has already been learnt, and provide motivation to discover more of the subject than can be covered in a single introduction.
  

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Review: Probability with Martingales

User Review  - Fausto Saleri - Goodreads

Inefficient, almost useless for any student. Notations are confuse, theorems are basically left to the reader; the choice behind the appendix is simply wrong, because you need to read it to go through ... Read full review

Review: Probability with Martingales

User Review  - Fausto Saleri - Goodreads

Inefficient, almost useless for any student. Notations are confuse, theorems are basically left to the reader; the choice behind the appendix is simply wrong, because you need to read it to go through ... Read full review

Contents

More about exercises In compiling Chapter E which consists exactly
4
of nth generation Zn 0 3 Use of conditional expectations 0 4 Extinction
10
Events
23
First BorelCantelli Lemma BCl 2 8 Definitions liminfEnEnev
27
Integration
49
Introductory remarks 6 1 Definition of expectation 6 2 Convergence
69
An Easy Strong Law
71
rule for measures Probability theory supplements that with the multipli
83
Martingales bounded in C2
110
Uniform Integrability
126
5 Martingale proof of the Strong Law 14 6 Doobs Sub
150
CHARACTERISTIC FUNCTIONS
172
The Central Limit Theorem
185
Appendix to Chapter 3
205
Appendix to Chapter 0
214
References
243

Kolmogorov 1933 9 3 The intuitive meaning 9 4 Conditional
92
The Convergence Theorem
106

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About the author (1991)

Williams teaches in the Performance Studies program at Victoria University, Melbourne. He is also a theater director.

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