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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Produktdetaljer
ISBN
9781139632263
Publisert
2014
Utgiver
Vendor
Cambridge University Press
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter