Probability essentials
type: Item
instance of: scholarly article
title: Probability essentials
zbMATH Open document ID: 0968.60003
author: Jean Jacod
author: Philip Protter
published in: Universitext
publication date: 2000-01-20T00:00:00Z
review text: This book is based on lectures held by both authors through many years. It is condensed to the ``essentials'' of probability theory and founded on measure theory which can be lectured in a one-semester course. The two topics are developed parallel, where the probabilistic line is the leading one, and where only the necessary tools from measure theory are presented. The authors have found a way to give a relatively short but highly concentrated course on probability theory on a mathematical level that remains understandable not only for mathematicians but also for students and scientists from engineering, economics and other fields. On the other hand, it is mathematically deep enough to open the door to a study of advanced applications of probability theory in other sciences, which use e.g. stochastic processes, martingales, Brownian motion, Itô calculus and so on. The content follows the usual line first: From discrete to general probability spaces, in particular on \(R_1\), \(R_n\), random variables and their distributions, moments, characteristic functions, convergence of random variables, laws of large numbers, central limit theorems, \(L^2\)-theory. Then it provides an introduction to conditional expectations, martingale theory and the Radon-Nikodým theorem, which meet with increasing interest in applications of probability theory. Many carefully chosen exercises following each of the 28 chapters strongly support the reader in understanding the matter. The book can be highly recommended to students as well as to lecturers.
reviewed by: Uwe Küchler
Mathematics Subject Classification ID: 60-01
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60E10
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 1391230
zbMATH Keywords: probability theory
zbMATH Keywords: random variables
zbMATH Keywords: distributions
zbMATH Keywords: law of large numbers
zbMATH Keywords: central limit theorem
zbMATH Keywords: martingales
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1391230