Probability Theory
Subtitle: Independence, Interchangeability, Martingales
Publisher: Springer New York
Published: 2012
Language: eng
Number of pages: 467
ISBN-13: 9781468405064
Subjects: Probabilities; Martingales (mathematics)
Description: This book is an introductory text on the beginning graduate level. Its subjects are the measure theoretical foundation of the theory and the main laws and theorems which emerge therefrom. The authors concentrate on certain important topics, primarily independence, interchangeability, and martingales. Particular emphasis is placed on stopping times, as tools in proving theorems as well as objects of interest in themselves. Among their applications is renewal theory; another useful application explained in this book is connected with the limiting behavior of random walks. A knowledge of measure theory is not assumed by the authors who intertwine measure and probability in their presentation as opposed to the customary sharp demarcation. The book can, however, be used as a text for students who have already been exposed to a course in measure theory. Many examples and exercises accompany the text.