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Probability with Martingales by David Williams Details

Probability theory is currently applied in a wide range of fields including physics, engineering, biology, economics and social sciences. This book is a modern, lively and rigorous account of Doob's…

Probability with Martingales synopsis

Probability theory is currently applied in a wide range of fields including physics, engineering, biology, economics and social sciences. This book is a modern, lively and rigorous account of Doob's theory of martingales at a separate time as its main theme.

It proves important results such as the powerful Kolmogorov Act of large numbers and the theory of the three series through Martingale techniques, and the theory of central reduction through the use of distinctive functions. The hallmark is their design to keep the flow of possibilities at a nice pace.

This is done by being selective rather than objective, providing only what is necessary to understand the basics; certain basic results of the measurement theory are assumed in the main text. These fully measured theoretical results have been demonstrated in the appendices, so that the book is completely independent.

The book is written for students, not for researchers, and has evolved over several years of class tests. Exercise plays a vital role.

Interesting and challenging problems, some with hints, solidifying what has already been learned, and providing the impetus to discover more of the subject than can be covered in one introduction.



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