Probability with Martingales

By: David Williams

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Paperback | 14 February 1991

At a Glance

Paperback
268 Pages

Dimensions(cm)
22.5 x 15.3 x 1.4

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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 role. 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.

Industry Reviews

'... one of the best introductions to Martingale theory.' Monatshefte fur Mathematik

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A branching-process example
Foundations
Measure spaces
Events
Random variables
Independence
Integration
Expectation
An easy strong law: product measure
Martingale Theory
Conditional expectation
Martingales
The convergence theorem
Martingales bounded in L2
Uniform integrability
UI martingales
Applications
Characteristic Functions
Basic properties of CFs
Weak convergence
The central limit theorem
Appendices
Exercises
Table of Contents provided by Publisher. All Rights Reserved.

Probability with Martingales

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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