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Derived from extensive teaching experience in Paris, this second edition now includes over 100 exercises in probability. New exercises have been added to reflect important areas of current research in probability theory, including infinite divisibility of stochastic processes, past-future martingales and fluctuation theory. For each exercise the authors provide detailed solutions as well as references for preliminary and further reading. There are also many insightful notes to motivate the student and set the exercises in context. Students will find these exercises extremely useful for easing the transition between simple and complex probabilistic frameworks. Indeed, many of the exercises here will lead the student on to frontier research topics in probability. Along the way, attention is drawn to a number of traps into which students of probability often fall. This book is ideal for independent study or as the companion to a course in advanced probability theory.
Class tested at the prestigious Paris school
Includes detailed solutions to all exercises as well as references to the literature and contextual notes
Second Edition includes new exercises, open problems and references to recent literature
Table of Contents
Preface to the Second Edition
Preface to the First Edition
1. Measure theory and probability
2. Independence and conditioning
3. Gaussian variables
4. Distributional computations
5. Convergence of random variables
6. Random processes
Where is the notion N discussed?
Final suggestions: how to go further?