Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, Via Conditioning. Loic Chaumont, Marc Yor

ISBN-13: 9781107606555 / Angielski / Miękka / 2012 / 300 str.

Loic Chaumont

Opis

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.

Recenzje

'This book, written in an inspiring style, can be used together with almost any advanced course and strongly recommend to doctoral and master students in the area of probability and stochastic processes. Young researchers and university teachers as well as professionals can benefit a lot from this book.' Jordan M. Stoyanov, Zentralblatt MATH

Spis treści

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.