Probability Theory I

This is a text for a one-quarter or one-semester course in probability, aimed at students who have done a year of calculus. The book is organised so a student can learn the fundamental ideas of probability from the first three chapters without reliance on calculus. Later chapters develop these ideas further using calculus tools. The book contains more than the usual number of examples worked out in detail.

The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems.

The theory of probability and mathematical statistics is becoming an indispensable discipline in many branches of science and engineering. This is caused by increasing significance of various uncertainties affecting performance of complex technological systems. Fundamental concepts and procedures used in analysis of these systems are often based on the theory of probability and mathematical statistics.

by Russell Lyons (Author), Yuval Peres (Author)

This new, thoroughly revised and expanded 3rd edition of a classic gives a comprehensive coverage of modern probability in a single book. It is a truly modern text, providing not only classical results but also material that will be important for future research. Much has been added to the previous edition, including eight entirely new chapters on subjects like random measures, Malliavin calculus, multivariate arrays, and stochastic differential geometry.

It is thought as necessary to write a Preface before a Book, as it is judged civil, when you invite a Friend to Dinner, to proffer him a Glass of Hock beforehand for a Whet. John Arbuthnot, from the preface to his translation of Huygens's "De Ratiociniis in Ludo Alooe". Prompted by an awareness of the importance of Bayesian ideas in modern statistical theory and practice, I decided some years ago to undertake a study of the development and growth of such ideas. At the time it seemed appropriate to begin such an investigation with an examination of Bayes's Essay towards solving a problem in the doctrine of chances and Laplace's Theorie analytique des probabilites, and then to pass swiftly on to a brief consideration of other nineteenth century works before turning to what would be the main topic of the treatise, videlicet the rise of Bayesian statis­ tics from the 1950's to the present day.

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