Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, via Conditioning

by Loïc Chaumont, Marc Yor

Overview

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.

Product Details

ISBN-13:	9781107606555
Publisher:	Cambridge University Press
Publication date:	07/19/2012
Series:	Cambridge Series in Statistical and Probabilistic Mathematics , #35
Edition description:	2nd Revised ed.
Pages:	300
Product dimensions:	7.01(w) x 10.00(h) x 0.63(d)

About the Author

Loïc Chaumont is a Professor in the Laboratoire Angevin de Recherche en Mathématiques (LAREMA) at Université d'Angers.

Marc Yor is a Professor in the Laboratoire de Probabilités et Modèles Aléatoires at Université Pierre et Marie Curie (Paris VI).

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?; References; Index.

Editorial Reviews

Of the first edition:
"...a very appealing and valuable book for independent study or as a companion book in advanced probability theory courses. Highly recommended."
Choice Magazine

Of the first edition:
"This is an excellent book, which should be in every library, and also on the bookshelf of anyone with interests in advanced probability and random processes."
SIAM Review

Of the first edition:
"...a magnificent resource, not just in terms of shearing recent research results to their core but in encouraging putative researchers to think of an interplay between finite and infinite dimensional viewpoints for a given problem. In that sense, the authors take us into the mind of the researcher...For beginning researchers in stochastic mathematics, this book comes highly recommended and libraries should obtain a copy."
Journal of the Royal Statistical Society

From the Publisher