Probability Theory with Applications

This book is a revised and expanded edition of a successful graduate and reference text. The material in the book is designed for a standard graduate course on probability theory, including some important applications. This new edition contains a detailed treatment of the core area of probability, and both structural and limit results are presented in full detail. Compared to the first edition, the material and presentation are better highlighted with several (small and large) alterations made to each chapter. Key features of the book include:

• Indicating the need for abstract theory even in applications and showing the inadequacy of existing results for certain apparently simple real-world problems

• Attempting to deal with the existence problems for various classes of random families that figure in the main results of the subject

• Providing a treatment of conditional expectations and of conditional probabilities that is more complete than in other existing textbooks

Since this is a textbook, essentially all proofs are given in complete detail (even at the risk of repetition), and some key results are given multiple proofs when each argument has something to contribute.

Contains a detailed treatment of the distinguishing features of probability theory - namely independence, conditioning and their many applications - leading to a comparative focus on Brownian motion and Poisson processes with extensions. Includes supplementary material: sn.pub/extras

Texte du rabat

Probability Theory and Applications is a revised and expanded edition of a successful graduate and reference text. The material in the book is designed for a standard graduate course on probability theory, including some important applications. This new edition contains a detailed treatment of the core area of probability, and both structural and limit results are presented in full detail. Compared to the first edition, the material and presentation are better highlighted with several (small and large) alterations made to each chapter. Key features of the book include:

• indicating the need for abstract theory even in applications and showing the inadequacy of existing results for certain apparently simple real-world problems;

• attempting to deal with the existence problems for various classes of random families that figure in the main results of the subject;

• providing a treatment of conditional expectations and of conditional probabilities that is more complete than in other existing textbooks.

Since this is a textbook, essentially all proofs are given in complete detail (even at the risk of repetition), and some key results are given multiple proofs when each argument has something to contribute.

Audience

This book is intended for graduate students and researchers interested in probability theory.

Contenu
Foundations.- Background Material and Preliminaries.- Independence and Strong Convergence.- Conditioning and Some Dependence Classes.- Analytical Theory.- Probability Distributions and Characteristic Functions.- Weak Limit Laws.- Applications.- Stopping Times, Martingales, and Convergence.- Limit Laws for Some Dependent Sequences.- A Glimpse of Stochastic Processes.